Key resources table.

Reagent type (species) or resource	Designation	Source or reference	Identifiers	Additional information
Genetic reagent (M. musculus)	B1-8ki	Lam et al., 1997		Dr. Rajewsky (Max Delbrück Center for Molecular Medicine)
Genetic reagent (M. musculus)	B1-8hiki	Shih et al., 2002	IMSR Cat# JAX:007775; RRID:IMSR_JAX:007775	Dr. Nussenzweig (The Rockefeller University)
Genetic reagent (M. musculus)	Bcl6flox	Kaji et al., 2012	IMSR Cat# RBRC05663; RRID:IMSR_RBRC05663	Dr. Takemori (RIKEN)
Genetic reagent (M. musculus)	Cd4-Cre	Lee et al., 2001	IMSR Cat# JAX:017336; RRID:IMSR_JAX:017336	Dr. Kubo (Tokyo University of Science)
Genetic reagent (M. musculus)	Cd40lg−/−	Xu et al., 1994	RRID:MGI:2449454	Dr. Flavell (Yale School of Medicine)
Genetic reagent (M. musculus)	Igκ−/−	Chen et al., 1993		Dr. Tsubata (Tokyo Medical and Dental University)
Genetic reagent (M. musculus)	OT-II	Barnden et al., 1998	IMSR Cat# JAX:004194; RRID:IMSR_JAX:004194	Dr. Kubo (Tokyo University of Science)
Cell line (M. musculus)	40LB	Nojima et al., 2011		Dr. Kitamura (Tokyo University of Science)
Cell line (M. musculus)	40LB-hi	Takatsuka et al., 2018		Dr. Kitamura (Tokyo University of Science)
Cell line (M. musculus)	40LB-lo	this paper		Dr. Kitamura (Tokyo University of Science)
Cell line (M. musculus)	40LB-mid	this paper		Dr. Kitamura (Tokyo University of Science)
Antibody	rat monoclonal anti-mouse CD40; FGK4.5	Bio X Cell	Bio X Cell Cat# BE0016-2; RRID:AB_1107647	250 μg
Antibody	armenian hamster monoclonal anti-mouse CD40L; MR-1	Noelle et al., 1992	ATCC Cat# HB-11048; RRID:CVCL_8964	1 mg/kg; Dr. Abe (Tokyo University of Science)
Sequence-based reagent	shRNA	this paper		See Supplementary file 1
Software, algorithm	FlowJo	https://www.flowjo.com/solutions/flowjo	RRID:SCR_008520
Software, algorithm	GraphPad Prism	https://graphpad.com	RRID:SCR_002798