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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 (32 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
3087.1.b.a	$3087$	$1$	3087.b	3.b	$2$	$12$	$12$	$1.541$	12.0.$\cdots$.1	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{8}+\cdots$
3087.1.d.a	$3087$	$1$	3087.d	7.b	$2$	$3$	$3$	$1.541$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{8}+\cdots$
3087.1.d.b	$3087$	$1$	3087.d	7.b	$2$	$6$	$6$	$1.541$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-7}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{8}+\cdots$
3087.1.m.a	$3087$	$1$	3087.m	7.d	$6$	$6$	$3$	$1.541$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{2}+\cdots$
3087.1.m.b	$3087$	$1$	3087.m	7.d	$6$	$12$	$6$	$1.541$	12.0.$\cdots$.2	$D_{14}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{9}q^{2}+(-\beta _{5}-\beta _{6})q^{4}+(\beta _{7}-\beta _{9}+\cdots)q^{8}+\cdots$
3087.1.q.a	$3087$	$1$	3087.q	21.h	$6$	$24$	$12$	$1.541$	24.0.$\cdots$.2	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1-\beta _{13}+\beta _{17})q^{4}+(-\beta _{2}+\cdots)q^{8}+\cdots$
3087.1.v.a	$3087$	$1$	3087.v	49.f	$14$	$6$	$1$	$1.541$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{14}q^{4}+(\zeta_{14}^{2}-\zeta_{14}^{6})q^{13}+\zeta_{14}^{2}q^{16}+\cdots$
3087.1.bj.a	$3087$	$1$	3087.bj	49.h	$42$	$12$	$1$	$1.541$	$\Q(\zeta_{21})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{42}^{16}q^{4}+(-\zeta_{42}^{12}+\zeta_{42}^{18}+\cdots)q^{13}+\cdots$
3087.1.bj.b	$3087$	$1$	3087.bj	49.h	$42$	$12$	$1$	$1.541$	$\Q(\zeta_{21})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{42}^{16}q^{4}+(\zeta_{42}^{12}-\zeta_{42}^{18})q^{13}+\cdots$
3087.1.bp.a	$3087$	$1$	3087.bp	343.j	$98$	$42$	$1$	$1.541$	$\Q(\zeta_{98})$	$D_{98}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{98}^{22}q^{4}+\zeta_{98}^{39}q^{7}+(-\zeta_{98}^{13}+\cdots)q^{13}+\cdots$
3087.2.a.a	$3087$	$2$	3087.a	1.a	$1$	$3$	$3$	$24.650$	$\Q(\zeta_{14})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$1$	$-3$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots$
3087.2.a.b	$3087$	$2$	3087.a	1.a	$1$	$3$	$3$	$24.650$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-2q^{5}+(1-2\beta _{1}+\cdots)q^{8}+\cdots$
3087.2.a.c	$3087$	$2$	3087.a	1.a	$1$	$3$	$3$	$24.650$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}+(1-2\beta _{1}+\cdots)q^{8}+\cdots$
3087.2.a.d	$3087$	$2$	3087.a	1.a	$1$	$3$	$3$	$24.650$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}+(1-2\beta _{1}+\cdots)q^{8}+\cdots$
3087.2.a.e	$3087$	$2$	3087.a	1.a	$1$	$3$	$3$	$24.650$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+2q^{5}+(1-2\beta _{1}+\cdots)q^{8}+\cdots$
3087.2.a.f	$3087$	$2$	3087.a	1.a	$1$	$3$	$3$	$24.650$	$\Q(\zeta_{14})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(4+\cdots)q^{8}+\cdots$
3087.2.a.g	$3087$	$2$	3087.a	1.a	$1$	$6$	$6$	$24.650$	6.6.35650048.1	$_{}$	None	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{4})q^{2}+(1-\beta _{2}-2\beta _{4})q^{4}+\cdots$
3087.2.a.h	$3087$	$2$	3087.a	1.a	$1$	$6$	$6$	$24.650$	$\Q(\zeta_{28})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{8}+\cdots$
3087.2.a.i	$3087$	$2$	3087.a	1.a	$1$	$6$	$6$	$24.650$	$\Q(\zeta_{28})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-\beta _{1}-\beta _{5})q^{2}+(1+2\beta _{2}+3\beta _{4}+\cdots)q^{4}+\cdots$
3087.2.a.j	$3087$	$2$	3087.a	1.a	$1$	$6$	$6$	$24.650$	6.6.1279733.1	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-11$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
3087.2.a.k	$3087$	$2$	3087.a	1.a	$1$	$6$	$6$	$24.650$	6.6.1279733.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$11$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
3087.2.a.l	$3087$	$2$	3087.a	1.a	$1$	$9$	$9$	$24.650$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-5$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{5}-\beta _{6})q^{4}+\cdots$
3087.2.a.m	$3087$	$2$	3087.a	1.a	$1$	$9$	$9$	$24.650$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-5$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{5}-\beta _{6})q^{4}+\cdots$
3087.2.a.n	$3087$	$2$	3087.a	1.a	$1$	$9$	$9$	$24.650$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
3087.2.a.o	$3087$	$2$	3087.a	1.a	$1$	$9$	$9$	$24.650$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
3087.2.a.p	$3087$	$2$	3087.a	1.a	$1$	$12$	$12$	$24.650$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{10}+\cdots)q^{5}+\cdots$
3087.2.a.q	$3087$	$2$	3087.a	1.a	$1$	$12$	$12$	$24.650$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{10})q^{5}+\cdots$
3087.2.a.r	$3087$	$2$	3087.a	1.a	$1$	$12$	$12$	$24.650$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{8}q^{2}+(2-\beta _{4}+2\beta _{6})q^{4}-\beta _{3}q^{5}+\cdots$
3087.2.c.a	$3087$	$2$	3087.c	21.c	$2$	$12$	$12$	$24.650$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{7}+\beta _{9}+\beta _{11})q^{2}+(-2-\beta _{6}+\cdots)q^{4}+\cdots$
3087.2.c.b	$3087$	$2$	3087.c	21.c	$2$	$12$	$12$	$24.650$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{3}+\beta _{7}-\beta _{9}-\beta _{11})q^{2}+(-2+\cdots)q^{4}+\cdots$
3087.2.c.c	$3087$	$2$	3087.c	21.c	$2$	$24$	$24$	$24.650$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3087.2.c.d	$3087$	$2$	3087.c	21.c	$2$	$48$	$48$	$24.650$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.