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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4152.2.a.a	$4152$	$2$	4152.a	1.a	$1$	$1$	$1$	$33.154$	$\Q$	None	✓	✓			4152.2.a.a	$1$	$1$	$0$	$-1$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots$
4152.2.a.b	$4152$	$2$	4152.a	1.a	$1$	$1$	$1$	$33.154$	$\Q$	None	✓	✓			4152.2.a.b	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+3q^{11}+2q^{13}+\cdots$
4152.2.a.c	$4152$	$2$	4152.a	1.a	$1$	$1$	$1$	$33.154$	$\Q$	None	✓	✓			4152.2.a.c	$1$	$0$	$0$	$1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots$
4152.2.a.d	$4152$	$2$	4152.a	1.a	$1$	$2$	$2$	$33.154$	$\Q(\sqrt{5}) $	None	✓	✓			4152.2.a.d	$1$	$0$	$0$	$2$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots$
4152.2.a.e	$4152$	$2$	4152.a	1.a	$1$	$3$	$3$	$33.154$	$\Q(\zeta_{14})^+$	None	✓	✓			4152.2.a.e	$1$	$0$	$0$	$-3$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{5}+q^{9}+(1-3\beta _{1}+\cdots)q^{11}+\cdots$
4152.2.a.f	$4152$	$2$	4152.a	1.a	$1$	$3$	$3$	$33.154$	3.3.169.1	None	✓	✓			4152.2.a.f	$1$	$0$	$0$	$-3$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}+(-2\beta _{1}+2\beta _{2})q^{7}+\cdots$
4152.2.a.g	$4152$	$2$	4152.a	1.a	$1$	$3$	$3$	$33.154$	3.3.257.1	None	✓	✓			4152.2.a.g	$1$	$1$	$0$	$3$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots$
4152.2.a.h	$4152$	$2$	4152.a	1.a	$1$	$4$	$4$	$33.154$	4.4.2777.1	None	✓	✓			4152.2.a.h	$1$	$1$	$0$	$4$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2-\beta _{2})q^{5}+q^{9}+(1+2\beta _{1}+\cdots)q^{11}+\cdots$
4152.2.a.i	$4152$	$2$	4152.a	1.a	$1$	$4$	$4$	$33.154$	4.4.23665.1	None	✓	✓			4152.2.a.i	$1$	$0$	$0$	$4$	$-4$	$16$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{3})q^{5}+4q^{7}+q^{9}+\cdots$
4152.2.a.j	$4152$	$2$	4152.a	1.a	$1$	$5$	$5$	$33.154$	5.5.245992.1	None	✓	✓	✓		4152.2.a.j	$1$	$1$	$0$	$5$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2}+\beta _{4})q^{7}+\cdots$
4152.2.a.k	$4152$	$2$	4152.a	1.a	$1$	$5$	$5$	$33.154$	5.5.1216489.1	None	✓	✓	✓		4152.2.a.k	$1$	$1$	$0$	$5$	$2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}-\beta _{4})q^{7}+\cdots$
4152.2.a.l	$4152$	$2$	4152.a	1.a	$1$	$6$	$6$	$33.154$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓		4152.2.a.l	$1$	$0$	$0$	$6$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}-\beta _{1}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
4152.2.a.m	$4152$	$2$	4152.a	1.a	$1$	$7$	$7$	$33.154$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		4152.2.a.m	$1$	$0$	$0$	$-7$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{6}q^{5}+(1+\beta _{4})q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$
4152.2.a.n	$4152$	$2$	4152.a	1.a	$1$	$7$	$7$	$33.154$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		4152.2.a.n	$1$	$0$	$0$	$-7$	$8$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{2}-\beta _{6})q^{5}+(1+\beta _{3})q^{7}+\cdots$
4152.2.a.o	$4152$	$2$	4152.a	1.a	$1$	$10$	$10$	$33.154$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		4152.2.a.o	$1$	$1$	$0$	$-10$	$5$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{4}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots$
4152.2.a.p	$4152$	$2$	4152.a	1.a	$1$	$11$	$11$	$33.154$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	4152.2.a.p	$1$	$1$	$0$	$-11$	$-11$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1})q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots$
4152.2.a.q	$4152$	$2$	4152.a	1.a	$1$	$13$	$13$	$33.154$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	4152.2.a.q	$1$	$0$	$0$	$13$	$7$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{7})q^{7}+q^{9}+\cdots$
4152.2.c.a	$4152$	$2$	4152.c	173.b	$2$	$2$	$2$	$33.154$	$\Q(\sqrt{-1}) $	None		✓			4152.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+iq^{5}+4iq^{7}-q^{9}+iq^{11}+\cdots$
4152.2.c.b	$4152$	$2$	4152.c	173.b	$2$	$40$	$40$	$33.154$		None		✓			4152.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4152.2.c.c	$4152$	$2$	4152.c	173.b	$2$	$44$	$44$	$33.154$		None		✓	✓		4152.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 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.