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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 (47 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
1859.1.c.a	$1859$	$1$	1859.c	11.b	$2$	$3$	$3$	$0.928$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
1859.1.c.b	$1859$	$1$	1859.c	11.b	$2$	$3$	$3$	$0.928$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$		$1$		$q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
1859.1.c.c	$1859$	$1$	1859.c	11.b	$2$	$4$	$4$	$0.928$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{6}+\cdots$
1859.1.d.a	$1859$	$1$	1859.d	143.d	$2$	$6$	$6$	$0.928$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-1+\beta _{2}+\beta _{4})q^{3}-q^{4}-\beta _{1}q^{5}+\cdots$
1859.1.i.a	$1859$	$1$	1859.i	143.i	$6$	$4$	$2$	$0.928$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$-1$	$1$	$0$	$-1$		$1$		$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$
1859.1.i.b	$1859$	$1$	1859.i	143.i	$6$	$4$	$2$	$0.928$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$1$	$1$	$0$	$1$		$1$		$q+(\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$
1859.1.i.c	$1859$	$1$	1859.i	143.i	$6$	$12$	$6$	$0.928$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(\beta _{4}+\beta _{5})q^{3}+(1-\beta _{7})q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$
1859.1.k.a	$1859$	$1$	1859.k	143.k	$6$	$6$	$3$	$0.928$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$-2$	$0$		$1$		$q+\beta _{4}q^{3}-\beta _{5}q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
1859.1.k.b	$1859$	$1$	1859.k	143.k	$6$	$6$	$3$	$0.928$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$2$	$0$		$1$		$q+\beta _{4}q^{3}-\beta _{5}q^{4}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
1859.1.k.c	$1859$	$1$	1859.k	143.k	$6$	$8$	$4$	$0.928$	8.0.12960000.1	$D_{5}$	$\Q(\sqrt{-143}) $	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-\beta _{3}-\beta _{6}-\beta _{7})q^{2}+(1-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
1859.2.a.a	$1859$	$2$	1859.a	1.a	$1$	$1$	$1$	$14.844$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots$
1859.2.a.b	$1859$	$2$	1859.a	1.a	$1$	$1$	$1$	$14.844$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+2q^{7}+\cdots$
1859.2.a.c	$1859$	$2$	1859.a	1.a	$1$	$2$	$2$	$14.844$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots$
1859.2.a.d	$1859$	$2$	1859.a	1.a	$1$	$2$	$2$	$14.844$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots$
1859.2.a.e	$1859$	$2$	1859.a	1.a	$1$	$3$	$3$	$14.844$	3.3.756.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}-q^{4}+(-1-\beta _{2})q^{5}+\cdots$
1859.2.a.f	$1859$	$2$	1859.a	1.a	$1$	$3$	$3$	$14.844$	3.3.361.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1859.2.a.g	$1859$	$2$	1859.a	1.a	$1$	$3$	$3$	$14.844$	3.3.361.1	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$
1859.2.a.h	$1859$	$2$	1859.a	1.a	$1$	$3$	$3$	$14.844$	3.3.756.1	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}-q^{4}+(1+\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots$
1859.2.a.i	$1859$	$2$	1859.a	1.a	$1$	$4$	$4$	$14.844$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots$
1859.2.a.j	$1859$	$2$	1859.a	1.a	$1$	$6$	$6$	$14.844$	6.6.84512328.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1859.2.a.k	$1859$	$2$	1859.a	1.a	$1$	$6$	$6$	$14.844$	6.6.28561300.1	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-6$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1859.2.a.l	$1859$	$2$	1859.a	1.a	$1$	$6$	$6$	$14.844$	6.6.28561300.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1859.2.a.m	$1859$	$2$	1859.a	1.a	$1$	$6$	$6$	$14.844$	6.6.194616205.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1859.2.a.n	$1859$	$2$	1859.a	1.a	$1$	$6$	$6$	$14.844$	6.6.84512328.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1859.2.a.o	$1859$	$2$	1859.a	1.a	$1$	$8$	$8$	$14.844$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-8$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
1859.2.a.p	$1859$	$2$	1859.a	1.a	$1$	$8$	$8$	$14.844$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$8$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
1859.2.a.q	$1859$	$2$	1859.a	1.a	$1$	$9$	$9$	$14.844$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-5$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots$
1859.2.a.r	$1859$	$2$	1859.a	1.a	$1$	$9$	$9$	$14.844$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-5$	$4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots$
1859.2.a.s	$1859$	$2$	1859.a	1.a	$1$	$21$	$21$	$14.844$		$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$-7$	$-1$	$-$		$\mathrm{SU}(2)$
1859.2.a.t	$1859$	$2$	1859.a	1.a	$1$	$21$	$21$	$14.844$		$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$7$	$1$	$-$		$\mathrm{SU}(2)$
1859.4.a.a	$1859$	$4$	1859.a	1.a	$1$	$2$	$2$	$109.685$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$-2$	$-20$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots$
1859.4.a.b	$1859$	$4$	1859.a	1.a	$1$	$4$	$4$	$109.685$	4.4.297133.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$6$	$17$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
1859.4.a.c	$1859$	$4$	1859.a	1.a	$1$	$6$	$6$	$109.685$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$-6$	$8$	$53$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
1859.4.a.d	$1859$	$4$	1859.a	1.a	$1$	$9$	$9$	$109.685$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$8$	$-30$	$-25$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
1859.4.a.e	$1859$	$4$	1859.a	1.a	$1$	$11$	$11$	$109.685$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-6$	$6$	$4$	$-45$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots$
1859.4.a.f	$1859$	$4$	1859.a	1.a	$1$	$17$	$17$	$109.685$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$-6$	$-16$	$6$	$-$	$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1859.4.a.g	$1859$	$4$	1859.a	1.a	$1$	$17$	$17$	$109.685$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$-24$	$-62$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1859.4.a.h	$1859$	$4$	1859.a	1.a	$1$	$17$	$17$	$109.685$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-6$	$24$	$62$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots$
1859.4.a.i	$1859$	$4$	1859.a	1.a	$1$	$17$	$17$	$109.685$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$-6$	$16$	$-6$	$+$	$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots$
1859.4.a.j	$1859$	$4$	1859.a	1.a	$1$	$18$	$18$	$109.685$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-20$	$-28$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1859.4.a.k	$1859$	$4$	1859.a	1.a	$1$	$18$	$18$	$109.685$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$20$	$28$	$+$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots$
1859.4.a.l	$1859$	$4$	1859.a	1.a	$1$	$36$	$36$	$109.685$		$_{}$	None	None	✓	$1$	$1$	$-4$	$12$	$-40$	$-56$	$-$		$\mathrm{SU}(2)$
1859.4.a.m	$1859$	$4$	1859.a	1.a	$1$	$36$	$36$	$109.685$		$_{}$	None	None	✓	$1$	$0$	$4$	$12$	$40$	$56$	$+$		$\mathrm{SU}(2)$
1859.4.a.n	$1859$	$4$	1859.a	1.a	$1$	$39$	$39$	$109.685$		$_{}$	None	None	✓	$1$	$1$	$0$	$-23$	$-23$	$4$	$-$		$\mathrm{SU}(2)$
1859.4.a.o	$1859$	$4$	1859.a	1.a	$1$	$39$	$39$	$109.685$		$_{}$	None	None	✓	$1$	$1$	$0$	$-23$	$23$	$-4$	$-$		$\mathrm{SU}(2)$
1859.4.a.p	$1859$	$4$	1859.a	1.a	$1$	$51$	$51$	$109.685$		$_{}$	None	None	✓	$1$	$0$	$0$	$21$	$-41$	$-4$	$+$		$\mathrm{SU}(2)$
1859.4.a.q	$1859$	$4$	1859.a	1.a	$1$	$51$	$51$	$109.685$		$_{}$	None	None	✓	$1$	$0$	$0$	$21$	$41$	$4$	$+$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.