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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 (31 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
1359.1.d.a	$1359$	$1$	1359.d	151.b	$2$	$1$	$1$	$0.678$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-151}) $	$\Q(\sqrt{453}) $	✓	✓			1359.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+q^{16}+2q^{19}-q^{25}+2q^{31}+\cdots$
1359.1.d.b	$1359$	$1$	1359.d	151.b	$2$	$3$	$3$	$0.678$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓				151.1.b.a	$2$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
1359.1.d.c	$1359$	$1$	1359.d	151.b	$2$	$6$	$6$	$0.678$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-151}) $	None	✓	✓	✓		1359.1.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots$
1359.1.x.a	$1359$	$1$	1359.x	151.f	$10$	$4$	$1$	$0.678$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1359.1.x.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+(\zeta_{10}+\zeta_{10}^{2})q^{7}+(-\zeta_{10}+\zeta_{10}^{3}+\cdots)q^{13}+\cdots$
1359.1.bp.a	$1359$	$1$	1359.bp	151.j	$50$	$20$	$1$	$0.678$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1359.1.bp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{50}^{20}q^{4}+(\zeta_{50}^{8}-\zeta_{50}^{14})q^{7}+\cdots$
1359.2.a.a	$1359$	$2$	1359.a	1.a	$1$	$2$	$2$	$10.852$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				453.2.a.d	$1$	$1$	$-3$	$0$	$3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(2-\beta )q^{5}+\cdots$
1359.2.a.b	$1359$	$2$	1359.a	1.a	$1$	$2$	$2$	$10.852$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				453.2.a.c	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-2q^{5}+q^{7}-\beta q^{8}-2\beta q^{10}+\cdots$
1359.2.a.c	$1359$	$2$	1359.a	1.a	$1$	$2$	$2$	$10.852$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				453.2.a.b	$1$	$1$	$1$	$0$	$1$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}-3q^{7}+\cdots$
1359.2.a.d	$1359$	$2$	1359.a	1.a	$1$	$2$	$2$	$10.852$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				453.2.a.a	$1$	$0$	$3$	$0$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(-2+\beta )q^{5}+\cdots$
1359.2.a.e	$1359$	$2$	1359.a	1.a	$1$	$3$	$3$	$10.852$	3.3.257.1	$_{}$	None	None	✓				151.2.a.b	$1$	$1$	$0$	$0$	$-5$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
1359.2.a.f	$1359$	$2$	1359.a	1.a	$1$	$3$	$3$	$10.852$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				453.2.a.e	$1$	$0$	$1$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-\beta _{1}+2\beta _{2})q^{5}+\cdots$
1359.2.a.g	$1359$	$2$	1359.a	1.a	$1$	$3$	$3$	$10.852$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				151.2.a.a	$1$	$0$	$2$	$0$	$7$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(3+\cdots)q^{5}+\cdots$
1359.2.a.h	$1359$	$2$	1359.a	1.a	$1$	$5$	$5$	$10.852$	5.5.1190005.1	$_{}$	None	None	✓				453.2.a.f	$1$	$0$	$3$	$0$	$4$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
1359.2.a.i	$1359$	$2$	1359.a	1.a	$1$	$6$	$6$	$10.852$	6.6.4838537.1	$_{}$	None	None	✓		✓		151.2.a.c	$1$	$1$	$-1$	$0$	$-6$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
1359.2.a.j	$1359$	$2$	1359.a	1.a	$1$	$6$	$6$	$10.852$	6.6.3356224.1	$_{}$	None	None	✓	✓	✓	✓	1359.2.a.j	$2$	$1$	$0$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{4}+\beta _{5})q^{5}+\cdots$
1359.2.a.k	$1359$	$2$	1359.a	1.a	$1$	$6$	$6$	$10.852$	6.6.19783872.1	$_{}$	None	None	✓	✓			1359.2.a.k	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}+2\beta _{3}q^{7}+\cdots$
1359.2.a.l	$1359$	$2$	1359.a	1.a	$1$	$9$	$9$	$10.852$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓		✓		453.2.a.g	$1$	$0$	$-6$	$0$	$2$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1+\beta _{2}+\beta _{3})q^{4}+\cdots$
1359.2.a.m	$1359$	$2$	1359.a	1.a	$1$	$14$	$14$	$10.852$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	✓	✓		1359.2.a.m	$2$	$0$	$0$	$0$	$0$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{5}-\beta _{6})q^{4}+\beta _{12}q^{5}+\cdots$
1359.2.b.a	$1359$	$2$	1359.b	453.b	$2$	$24$	$24$	$10.852$		$_{}$	None	None		✓			1359.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1359.2.b.b	$1359$	$2$	1359.b	453.b	$2$	$28$	$28$	$10.852$		$_{}$	$\Q(\sqrt{-151}) $	None		✓	✓		1359.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{2}]$
1359.2.s.a	$1359$	$2$	1359.s	453.i	$6$	$100$	$50$	$10.852$		$_{}$	None	None		✓	✓	✓	1359.2.s.a	$4$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{6}]$
1359.3.c.a	$1359$	$3$	1359.c	3.b	$2$	$100$	$100$	$37.030$		$_{}$	None	None		✓	✓	✓	1359.3.c.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1359.4.a.a	$1359$	$4$	1359.a	1.a	$1$	$1$	$1$	$80.184$	$\Q$	$_{}$	None	None	✓				453.4.a.a	$1$	$0$	$3$	$0$	$19$	$-32$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+q^{4}+19q^{5}-2^{5}q^{7}-21q^{8}+\cdots$
1359.4.a.b	$1359$	$4$	1359.a	1.a	$1$	$14$	$14$	$80.184$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓				453.4.a.b	$1$	$1$	$8$	$0$	$20$	$-79$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
1359.4.a.c	$1359$	$4$	1359.a	1.a	$1$	$15$	$15$	$80.184$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓				151.4.a.a	$1$	$0$	$6$	$0$	$61$	$-26$	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(4-\beta _{1}+\cdots)q^{5}+\cdots$
1359.4.a.d	$1359$	$4$	1359.a	1.a	$1$	$17$	$17$	$80.184$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓				453.4.a.c	$1$	$1$	$-6$	$0$	$-20$	$19$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{12}+\cdots)q^{5}+\cdots$
1359.4.a.e	$1359$	$4$	1359.a	1.a	$1$	$21$	$21$	$80.184$		$_{}$	None	None	✓				453.4.a.d	$1$	$0$	$8$	$0$	$20$	$-37$	$+$		$\mathrm{SU}(2)$
1359.4.a.f	$1359$	$4$	1359.a	1.a	$1$	$22$	$22$	$80.184$		$_{}$	None	None	✓		✓		151.4.a.b	$1$	$1$	$-6$	$0$	$-59$	$30$	$-$		$\mathrm{SU}(2)$
1359.4.a.g	$1359$	$4$	1359.a	1.a	$1$	$23$	$23$	$80.184$		$_{}$	None	None	✓		✓		453.4.a.e	$1$	$0$	$-9$	$0$	$-39$	$121$	$+$		$\mathrm{SU}(2)$
1359.4.a.h	$1359$	$4$	1359.a	1.a	$1$	$30$	$30$	$80.184$		$_{}$	None	None	✓	✓	✓	✓	1359.4.a.h	$2$	$1$	$0$	$0$	$0$	$-52$	$-$		$\mathrm{SU}(2)$
1359.4.a.i	$1359$	$4$	1359.a	1.a	$1$	$44$	$44$	$80.184$		$_{}$	None	None	✓	✓	✓	✓	1359.4.a.i	$2$	$0$	$0$	$0$	$0$	$60$	$+$		$\mathrm{SU}(2)$

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