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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (20 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2679.1.h.a	$2679$	$1$	2679.h	2679.h	$2$	$6$	$6$	$1.337$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2679}) $	None	✓	✓			2679.1.h.a	$2$	$0$	$-1$	$6$	$-1$	$-1$		$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
2679.1.h.b	$2679$	$1$	2679.h	2679.h	$2$	$6$	$6$	$1.337$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2679}) $	None	✓	✓			2679.1.h.a	$2$	$0$	$-1$	$6$	$1$	$-1$		$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
2679.1.h.c	$2679$	$1$	2679.h	2679.h	$2$	$6$	$6$	$1.337$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2679}) $	None	✓	✓			2679.1.h.a	$2$	$0$	$1$	$-6$	$-1$	$-1$		$1$		$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
2679.1.h.d	$2679$	$1$	2679.h	2679.h	$2$	$6$	$6$	$1.337$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2679}) $	None	✓	✓			2679.1.h.a	$2$	$0$	$1$	$-6$	$1$	$-1$		$1$		$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
2679.2.a.a	$2679$	$2$	2679.a	1.a	$1$	$1$	$1$	$21.392$	$\Q$	$_{}$	None	None	✓	✓			2679.2.a.a	$1$	$2$	$-2$	$-1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots$
2679.2.a.b	$2679$	$2$	2679.a	1.a	$1$	$1$	$1$	$21.392$	$\Q$	$_{}$	None	None	✓	✓			2679.2.a.b	$1$	$1$	$-2$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots$
2679.2.a.c	$2679$	$2$	2679.a	1.a	$1$	$1$	$1$	$21.392$	$\Q$	$_{}$	None	None	✓	✓			2679.2.a.c	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots$
2679.2.a.d	$2679$	$2$	2679.a	1.a	$1$	$1$	$1$	$21.392$	$\Q$	$_{}$	None	None	✓	✓			2679.2.a.d	$1$	$1$	$2$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots$
2679.2.a.e	$2679$	$2$	2679.a	1.a	$1$	$3$	$3$	$21.392$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓			2679.2.a.e	$1$	$1$	$0$	$-3$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
2679.2.a.f	$2679$	$2$	2679.a	1.a	$1$	$3$	$3$	$21.392$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓			2679.2.a.f	$1$	$1$	$0$	$3$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\beta _{2})q^{5}+\cdots$
2679.2.a.g	$2679$	$2$	2679.a	1.a	$1$	$4$	$4$	$21.392$	4.4.1957.1	$_{}$	None	None	✓	✓			2679.2.a.g	$1$	$1$	$0$	$-4$	$5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{2}-q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
2679.2.a.h	$2679$	$2$	2679.a	1.a	$1$	$4$	$4$	$21.392$	4.4.2777.1	$_{}$	None	None	✓	✓			2679.2.a.h	$1$	$1$	$0$	$4$	$2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{3})q^{4}+\beta _{3}q^{5}+\cdots$
2679.2.a.i	$2679$	$2$	2679.a	1.a	$1$	$6$	$6$	$21.392$	6.6.5476681.1	$_{}$	None	None	✓	✓	✓		2679.2.a.i	$1$	$1$	$4$	$-6$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{4})q^{2}-q^{3}+(1+\beta _{2}+2\beta _{4}+\cdots)q^{4}+\cdots$
2679.2.a.j	$2679$	$2$	2679.a	1.a	$1$	$7$	$7$	$21.392$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		2679.2.a.j	$1$	$1$	$-4$	$7$	$-10$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2679.2.a.k	$2679$	$2$	2679.a	1.a	$1$	$7$	$7$	$21.392$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		2679.2.a.k	$1$	$1$	$-2$	$-7$	$6$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots$
2679.2.a.l	$2679$	$2$	2679.a	1.a	$1$	$7$	$7$	$21.392$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		2679.2.a.l	$1$	$1$	$-2$	$7$	$-6$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
2679.2.a.m	$2679$	$2$	2679.a	1.a	$1$	$23$	$23$	$21.392$		$_{}$	None	None	✓	✓	✓		2679.2.a.m	$1$	$0$	$2$	$-23$	$9$	$5$	$-$		$\mathrm{SU}(2)$
2679.2.a.n	$2679$	$2$	2679.a	1.a	$1$	$23$	$23$	$21.392$		$_{}$	None	None	✓	✓	✓	✓	2679.2.a.n	$1$	$0$	$5$	$23$	$12$	$-2$	$-$		$\mathrm{SU}(2)$
2679.2.a.o	$2679$	$2$	2679.a	1.a	$1$	$24$	$24$	$21.392$		$_{}$	None	None	✓	✓	✓	✓	2679.2.a.o	$1$	$0$	$2$	$-24$	$-2$	$6$	$-$		$\mathrm{SU}(2)$
2679.2.a.p	$2679$	$2$	2679.a	1.a	$1$	$24$	$24$	$21.392$		$_{}$	None	None	✓	✓	✓	✓	2679.2.a.p	$1$	$0$	$6$	$24$	$10$	$6$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.