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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 (20 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3481.1.b.a	$3481$	$1$	3481.b	59.b	$2$	$2$	$2$	$1.737$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$2$	$-2$	$-2$		$1$		$q-\beta q^{2}+q^{3}-q^{4}-q^{5}-\beta q^{6}-q^{7}+\cdots$
3481.1.d.a	$3481$	$1$	3481.d	59.d	$58$	$28$	$1$	$1.737$	$\Q(\zeta_{58})$	$D_{3}$	$\Q(\sqrt{-59}) $	None		$56$	$0$	$0$	$1$	$1$	$1$		$1$		$q+\zeta_{58}^{17}q^{3}-\zeta_{58}^{3}q^{4}+\zeta_{58}^{9}q^{5}+\cdots$
3481.1.d.b	$3481$	$1$	3481.d	59.d	$58$	$56$	$2$	$1.737$	$\mathbb{Q}[x]/(x^{56} - \cdots)$	$S_{4}$	None	None		$56$	$0$	$0$	$-2$	$2$	$2$		$1$		$q-\beta _{31}q^{2}-\beta _{42}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{5}+\cdots$
3481.2.a.a	$3481$	$2$	3481.a	1.a	$1$	$2$	$2$	$27.796$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$-2$	$-2$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+3q^{4}-q^{5}+\beta q^{6}-3q^{7}+\cdots$
3481.2.a.b	$3481$	$2$	3481.a	1.a	$1$	$2$	$2$	$27.796$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$4$	$-6$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2q^{3}+q^{4}-3q^{5}+2\beta q^{6}+\cdots$
3481.2.a.c	$3481$	$2$	3481.a	1.a	$1$	$3$	$3$	$27.796$	3.3.1593.1	$_{}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-\beta _{1}q^{3}-2q^{4}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
3481.2.a.d	$3481$	$2$	3481.a	1.a	$1$	$5$	$5$	$27.796$	5.5.138136.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}+\cdots$
3481.2.a.e	$3481$	$2$	3481.a	1.a	$1$	$5$	$5$	$27.796$	5.5.245992.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\cdots$
3481.2.a.f	$3481$	$2$	3481.a	1.a	$1$	$5$	$5$	$27.796$	5.5.245992.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\cdots$
3481.2.a.g	$3481$	$2$	3481.a	1.a	$1$	$6$	$6$	$27.796$	6.6.303369408.1	$_{}$	None	None	✓	$2$	$1$	$0$	$-6$	$2$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots$
3481.2.a.h	$3481$	$2$	3481.a	1.a	$1$	$8$	$8$	$27.796$	$\Q(\zeta_{60})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$-8$	$-18$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{6})q^{2}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$
3481.2.a.i	$3481$	$2$	3481.a	1.a	$1$	$8$	$8$	$27.796$	$\Q(\zeta_{60})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$-4$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
3481.2.a.j	$3481$	$2$	3481.a	1.a	$1$	$12$	$12$	$27.796$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots$
3481.2.a.k	$3481$	$2$	3481.a	1.a	$1$	$12$	$12$	$27.796$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$4$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots$
3481.2.a.l	$3481$	$2$	3481.a	1.a	$1$	$16$	$16$	$27.796$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$2$	$1$	$0$	$4$	$6$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{10}-\beta _{12})q^{2}+(1+\beta _{6}-\beta _{13}+\cdots)q^{3}+\cdots$
3481.2.a.m	$3481$	$2$	3481.a	1.a	$1$	$20$	$20$	$27.796$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-5$	$4$	$11$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{15}+\cdots)q^{5}+\cdots$
3481.2.a.n	$3481$	$2$	3481.a	1.a	$1$	$20$	$20$	$27.796$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$2$	$1$	$0$	$-8$	$-8$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{17}q^{3}+(1+\beta _{13}-\beta _{14}+\cdots)q^{4}+\cdots$
3481.2.a.o	$3481$	$2$	3481.a	1.a	$1$	$20$	$20$	$27.796$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$4$	$11$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{15}+\cdots)q^{5}+\cdots$
3481.2.a.p	$3481$	$2$	3481.a	1.a	$1$	$56$	$56$	$27.796$		$_{}$	None	None	✓	$1$	$1$	$-13$	$3$	$2$	$3$	$+$		$\mathrm{SU}(2)$
3481.2.a.q	$3481$	$2$	3481.a	1.a	$1$	$56$	$56$	$27.796$		$_{}$	None	None	✓	$1$	$0$	$13$	$3$	$2$	$3$	$-$		$\mathrm{SU}(2)$

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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.