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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 (35 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
1340.1.t.a	$1340$	$1$	1340.t	1340.t	$6$	$2$	$1$	$0.669$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$2$	$1$		$1$		$q-\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}q^{6}+\cdots$
1340.1.t.b	$1340$	$1$	1340.t	1340.t	$6$	$2$	$1$	$0.669$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$2$	$-1$		$1$		$q+\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}q^{6}+\cdots$
1340.1.bb.a	$1340$	$1$	1340.bb	1340.ab	$22$	$10$	$1$	$0.669$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$-2$		$1$		$q-\zeta_{22}q^{2}+(\zeta_{22}^{4}+\zeta_{22}^{8})q^{3}+\zeta_{22}^{2}q^{4}+\cdots$
1340.1.bb.b	$1340$	$1$	1340.bb	1340.ab	$22$	$10$	$1$	$0.669$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$-1$	$2$		$1$		$q+\zeta_{22}q^{2}+(-\zeta_{22}^{4}-\zeta_{22}^{8})q^{3}+\zeta_{22}^{2}q^{4}+\cdots$
1340.1.bl.a	$1340$	$1$	1340.bl	1340.al	$66$	$20$	$1$	$0.669$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$-2$	$1$		$1$		$q+\zeta_{66}^{31}q^{2}+(\zeta_{66}^{17}+\zeta_{66}^{25})q^{3}+\cdots$
1340.1.bl.b	$1340$	$1$	1340.bl	1340.al	$66$	$20$	$1$	$0.669$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$-2$	$-1$		$1$		$q-\zeta_{66}^{31}q^{2}+(-\zeta_{66}^{17}-\zeta_{66}^{25}+\cdots)q^{3}+\cdots$
1340.2.a.a	$1340$	$2$	1340.a	1.a	$1$	$1$	$1$	$10.700$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$
1340.2.a.b	$1340$	$2$	1340.a	1.a	$1$	$1$	$1$	$10.700$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}-6q^{11}+2q^{13}+\cdots$
1340.2.a.c	$1340$	$2$	1340.a	1.a	$1$	$1$	$1$	$10.700$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+5q^{7}-2q^{9}+2q^{13}+\cdots$
1340.2.a.d	$1340$	$2$	1340.a	1.a	$1$	$2$	$2$	$10.700$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$
1340.2.a.e	$1340$	$2$	1340.a	1.a	$1$	$2$	$2$	$10.700$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+2q^{7}+(1+2\beta )q^{9}+\cdots$
1340.2.a.f	$1340$	$2$	1340.a	1.a	$1$	$3$	$3$	$10.700$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+q^{5}+(1-3\beta _{1}+2\beta _{2})q^{7}+\cdots$
1340.2.a.g	$1340$	$2$	1340.a	1.a	$1$	$3$	$3$	$10.700$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots$
1340.2.a.h	$1340$	$2$	1340.a	1.a	$1$	$4$	$4$	$10.700$	4.4.60513.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
1340.2.a.i	$1340$	$2$	1340.a	1.a	$1$	$5$	$5$	$10.700$	5.5.1465016.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-5$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-2+\beta _{2})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
1340.2.d.a	$1340$	$2$	1340.d	5.b	$2$	$2$	$2$	$10.700$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-2+i)q^{5}+3iq^{7}+2q^{9}+\cdots$
1340.2.d.b	$1340$	$2$	1340.d	5.b	$2$	$8$	$8$	$10.700$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$16$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+(2-\beta _{5})q^{5}+(-\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots$
1340.2.d.c	$1340$	$2$	1340.d	5.b	$2$	$24$	$24$	$10.700$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-10$	$0$			$\mathrm{SU}(2)[C_{2}]$
1340.2.i.a	$1340$	$2$	1340.i	67.c	$3$	$2$	$1$	$10.700$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{3}+q^{5}+\zeta_{6}q^{7}-2q^{9}+6\zeta_{6}q^{11}+\cdots$
1340.2.i.b	$1340$	$2$	1340.i	67.c	$3$	$8$	$4$	$10.700$	8.0.5808268944.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$-8$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{3}-q^{5}+(\beta _{1}-\beta _{6})q^{7}+\beta _{2}q^{9}+\cdots$
1340.2.i.c	$1340$	$2$	1340.i	67.c	$3$	$16$	$8$	$10.700$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-16$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{3}-q^{5}+\beta _{11}q^{7}+(2+\beta _{2})q^{9}+\cdots$
1340.2.i.d	$1340$	$2$	1340.i	67.c	$3$	$18$	$9$	$10.700$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$18$	$3$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{3}+q^{5}-\beta _{10}q^{7}+(1+\cdots)q^{9}+\cdots$
1340.2.j.a	$1340$	$2$	1340.j	335.f	$4$	$68$	$34$	$10.700$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1340.2.o.a	$1340$	$2$	1340.o	335.i	$6$	$68$	$34$	$10.700$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
1340.3.b.a	$1340$	$3$	1340.b	67.b	$2$	$2$	$2$	$36.512$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{5}-\beta q^{7}+4q^{9}+6\beta q^{11}+\cdots$
1340.3.b.b	$1340$	$3$	1340.b	67.b	$2$	$42$	$42$	$36.512$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1340.3.g.a	$1340$	$3$	1340.g	335.d	$2$	$68$	$68$	$36.512$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1340.3.q.a	$1340$	$3$	1340.q	67.d	$6$	$92$	$46$	$36.512$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$18$			$\mathrm{SU}(2)[C_{6}]$
1340.4.a.a	$1340$	$4$	1340.a	1.a	$1$	$1$	$1$	$79.063$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-5$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}-5q^{5}-2^{4}q^{7}-11q^{9}-2^{6}q^{11}+\cdots$
1340.4.a.b	$1340$	$4$	1340.a	1.a	$1$	$16$	$16$	$79.063$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-8$	$80$	$-43$	$-$	$2^{7}\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+5q^{5}+(-3-\beta _{8})q^{7}+(8+\cdots)q^{9}+\cdots$
1340.4.a.c	$1340$	$4$	1340.a	1.a	$1$	$16$	$16$	$79.063$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-80$	$-39$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-5q^{5}+(-2-\beta _{4})q^{7}+(11+\cdots)q^{9}+\cdots$
1340.4.a.d	$1340$	$4$	1340.a	1.a	$1$	$16$	$16$	$79.063$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$8$	$-80$	$43$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-5q^{5}+(3-\beta _{4})q^{7}+(8+\cdots)q^{9}+\cdots$
1340.4.a.e	$1340$	$4$	1340.a	1.a	$1$	$17$	$17$	$79.063$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$85$	$55$	$+$	$2^{8}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+5q^{5}+(3-\beta _{6})q^{7}+(11+\beta _{1}+\cdots)q^{9}+\cdots$
1340.4.d.a	$1340$	$4$	1340.d	5.b	$2$	$98$	$98$	$79.063$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-20$	$0$			$\mathrm{SU}(2)[C_{2}]$
1340.5.b.a	$1340$	$5$	1340.b	67.b	$2$	$92$	$92$	$138.516$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.