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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (21 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1334.2.a.a	$1334$	$2$	1334.a	1.a	$1$	$1$	$1$	$10.652$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-3q^{9}+2q^{11}+\cdots$
1334.2.a.b	$1334$	$2$	1334.a	1.a	$1$	$1$	$1$	$10.652$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-4q^{7}+\cdots$
1334.2.a.c	$1334$	$2$	1334.a	1.a	$1$	$1$	$1$	$10.652$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1334.2.a.d	$1334$	$2$	1334.a	1.a	$1$	$4$	$4$	$10.652$	4.4.37108.1	None	✓	$1$	$1$	$-4$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots$
1334.2.a.e	$1334$	$2$	1334.a	1.a	$1$	$4$	$4$	$10.652$	4.4.4352.1	None	✓	$1$	$1$	$4$	$-4$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1334.2.a.f	$1334$	$2$	1334.a	1.a	$1$	$5$	$5$	$10.652$	5.5.207184.1	None	✓	$1$	$1$	$-5$	$1$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots$
1334.2.a.g	$1334$	$2$	1334.a	1.a	$1$	$5$	$5$	$10.652$	5.5.978400.1	None	✓	$1$	$0$	$-5$	$1$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}+\beta _{4})q^{5}+\cdots$
1334.2.a.h	$1334$	$2$	1334.a	1.a	$1$	$5$	$5$	$10.652$	5.5.179024.1	None	✓	$1$	$1$	$5$	$-3$	$-5$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots$
1334.2.a.i	$1334$	$2$	1334.a	1.a	$1$	$8$	$8$	$10.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$4$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{4}q^{6}+\cdots$
1334.2.a.j	$1334$	$2$	1334.a	1.a	$1$	$9$	$9$	$10.652$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-9$	$-3$	$5$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{6})q^{5}+\beta _{1}q^{6}+\cdots$
1334.2.a.k	$1334$	$2$	1334.a	1.a	$1$	$10$	$10$	$10.652$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$5$	$-1$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots$
1334.2.c.a	$1334$	$2$	1334.c	29.b	$2$	$28$	$28$	$10.652$		None		$2$	$0$	$0$	$0$	$-2$	$16$			$\mathrm{SU}(2)[C_{2}]$
1334.2.c.b	$1334$	$2$	1334.c	29.b	$2$	$28$	$28$	$10.652$		None		$2$	$0$	$0$	$0$	$2$	$-8$			$\mathrm{SU}(2)[C_{2}]$
1334.4.a.a	$1334$	$4$	1334.a	1.a	$1$	$15$	$15$	$78.709$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$30$	$-18$	$-25$	$-55$	$-$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots$
1334.4.a.b	$1334$	$4$	1334.a	1.a	$1$	$17$	$17$	$78.709$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$1$	$-34$	$10$	$-25$	$-27$	$-$	$3$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
1334.4.a.c	$1334$	$4$	1334.a	1.a	$1$	$18$	$18$	$78.709$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$36$	$-3$	$0$	$-41$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{8})q^{5}+\cdots$
1334.4.a.d	$1334$	$4$	1334.a	1.a	$1$	$19$	$19$	$78.709$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$1$	$-38$	$-5$	$0$	$-13$	$-$	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}-\beta _{6}q^{5}+2\beta _{1}q^{6}+\cdots$
1334.4.a.e	$1334$	$4$	1334.a	1.a	$1$	$21$	$21$	$78.709$		None	✓	$1$	$0$	$-42$	$-5$	$0$	$15$	$+$		$\mathrm{SU}(2)$
1334.4.a.f	$1334$	$4$	1334.a	1.a	$1$	$21$	$21$	$78.709$		None	✓	$1$	$0$	$-42$	$-2$	$25$	$29$	$+$		$\mathrm{SU}(2)$
1334.4.a.g	$1334$	$4$	1334.a	1.a	$1$	$21$	$21$	$78.709$		None	✓	$1$	$0$	$42$	$18$	$25$	$57$	$+$		$\mathrm{SU}(2)$
1334.4.a.h	$1334$	$4$	1334.a	1.a	$1$	$22$	$22$	$78.709$		None	✓	$1$	$0$	$44$	$21$	$0$	$43$	$+$		$\mathrm{SU}(2)$

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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.