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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	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	71	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5041.2.a.a	$5041$	$2$	5041.a	1.a	$1$	$3$	$3$	$40.253$	3.3.257.1	None	✓				71.2.a.a	$1$	$0$	$-1$	$1$	$5$	$-2$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
5041.2.a.b	$5041$	$2$	5041.a	1.a	$1$	$3$	$3$	$40.253$	3.3.257.1	None	✓				71.2.a.b	$1$	$0$	$0$	$-1$	$-3$	$-2$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
5041.2.a.c	$5041$	$2$	5041.a	1.a	$1$	$4$	$4$	$40.253$	$\Q(\zeta_{24})^+$	None	✓	✓			5041.2.a.c	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots$
5041.2.a.d	$5041$	$2$	5041.a	1.a	$1$	$6$	$6$	$40.253$	6.6.3359232.1	None	✓	✓			5041.2.a.d	$2$	$1$	$-6$	$6$	$-6$	$0$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{4})q^{2}+(1-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
5041.2.a.e	$5041$	$2$	5041.a	1.a	$1$	$6$	$6$	$40.253$	6.6.1229312.1	None	✓	✓			5041.2.a.e	$2$	$1$	$4$	$-10$	$6$	$0$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{2}+(-2-\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
5041.2.a.f	$5041$	$2$	5041.a	1.a	$1$	$7$	$7$	$40.253$	7.7.$\cdots$.1	$\Q(\sqrt{-71}) $	✓	✓			5041.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
5041.2.a.g	$5041$	$2$	5041.a	1.a	$1$	$7$	$7$	$40.253$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓			5041.2.a.g	$1$	$0$	$2$	$1$	$-1$	$-3$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
5041.2.a.h	$5041$	$2$	5041.a	1.a	$1$	$7$	$7$	$40.253$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓			5041.2.a.g	$1$	$0$	$2$	$1$	$-1$	$3$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
5041.2.a.i	$5041$	$2$	5041.a	1.a	$1$	$10$	$10$	$40.253$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓				71.2.c.a	$1$	$1$	$2$	$2$	$-3$	$-3$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\cdots$
5041.2.a.j	$5041$	$2$	5041.a	1.a	$1$	$10$	$10$	$40.253$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓				71.2.c.a	$1$	$0$	$2$	$2$	$-3$	$3$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\cdots$
5041.2.a.k	$5041$	$2$	5041.a	1.a	$1$	$14$	$14$	$40.253$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓			5041.2.a.k	$2$	$0$	$0$	$6$	$6$	$0$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{2}-\beta _{1}q^{3}+(1-\beta _{6}-\beta _{8})q^{4}+\cdots$
5041.2.a.l	$5041$	$2$	5041.a	1.a	$1$	$15$	$15$	$40.253$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓				71.2.d.a	$1$	$1$	$2$	$2$	$-5$	$-5$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{7}-\beta _{10}+\cdots)q^{4}+\cdots$
5041.2.a.m	$5041$	$2$	5041.a	1.a	$1$	$15$	$15$	$40.253$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓				71.2.d.a	$1$	$0$	$2$	$2$	$-5$	$5$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{7}-\beta _{10}+\cdots)q^{4}+\cdots$
5041.2.a.n	$5041$	$2$	5041.a	1.a	$1$	$18$	$18$	$40.253$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓			5041.2.a.n	$1$	$0$	$6$	$3$	$6$	$-3$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$
5041.2.a.o	$5041$	$2$	5041.a	1.a	$1$	$18$	$18$	$40.253$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓			5041.2.a.n	$1$	$0$	$6$	$3$	$6$	$3$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$
5041.2.a.p	$5041$	$2$	5041.a	1.a	$1$	$20$	$20$	$40.253$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	✓			5041.2.a.p	$2$	$1$	$-4$	$-4$	$-12$	$0$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{9}q^{2}+\beta _{10}q^{3}+(1+\beta _{12}+\beta _{15}+\cdots)q^{4}+\cdots$
5041.2.a.q	$5041$	$2$	5041.a	1.a	$1$	$36$	$36$	$40.253$		None	✓	✓			5041.2.a.q	$2$	$0$	$0$	$6$	$12$	$0$	$-$	$-$		$\mathrm{SU}(2)$
5041.2.a.r	$5041$	$2$	5041.a	1.a	$1$	$60$	$60$	$40.253$		None	✓	✓			5041.2.a.r	$2$	$1$	$-12$	$-12$	$-24$	$0$	$+$	$+$		$\mathrm{SU}(2)$
5041.2.a.s	$5041$	$2$	5041.a	1.a	$1$	$60$	$60$	$40.253$		None	✓				71.2.g.a	$1$	$1$	$-2$	$-2$	$10$	$-25$	$+$	$+$		$\mathrm{SU}(2)$
5041.2.a.t	$5041$	$2$	5041.a	1.a	$1$	$60$	$60$	$40.253$		None	✓		✓		71.2.g.a	$1$	$0$	$-2$	$-2$	$10$	$25$	$-$	$-$		$\mathrm{SU}(2)$

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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.