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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 (1-50 of 76 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
875.1.c.a	$875$	$1$	875.c	35.c	$2$	$2$	$2$	$0.437$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-35}) $	None	✓	✓			875.1.d.a	$2$	$0$	$0$	$-1$	$0$	$2$		$1$		$q+(-1+\beta )q^{3}+q^{4}+q^{7}+(1-\beta )q^{9}+\cdots$
875.1.c.b	$875$	$1$	875.c	35.c	$2$	$2$	$2$	$0.437$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-35}) $	None	✓	✓			875.1.d.a	$2$	$0$	$0$	$1$	$0$	$-2$		$1$		$q+(1-\beta )q^{3}+q^{4}-q^{7}+(1-\beta )q^{9}+\cdots$
875.1.d.a	$875$	$1$	875.d	7.b	$2$	$4$	$4$	$0.437$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-35}) $	None		✓	✓	✓	875.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}-q^{4}+\beta _{3}q^{7}+\beta _{2}q^{9}+\beta _{2}q^{11}+\cdots$
875.2.a.a	$875$	$2$	875.a	1.a	$1$	$2$	$2$	$6.987$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			875.2.a.a	$1$	$1$	$-1$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
875.2.a.b	$875$	$2$	875.a	1.a	$1$	$2$	$2$	$6.987$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			875.2.a.b	$1$	$0$	$0$	$-3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(-1-\beta )q^{3}+3q^{4}+\cdots$
875.2.a.c	$875$	$2$	875.a	1.a	$1$	$2$	$2$	$6.987$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			875.2.a.b	$1$	$0$	$0$	$3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(2-\beta )q^{3}+3q^{4}+(4+\cdots)q^{6}+\cdots$
875.2.a.d	$875$	$2$	875.a	1.a	$1$	$2$	$2$	$6.987$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			875.2.a.a	$1$	$1$	$1$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
875.2.a.e	$875$	$2$	875.a	1.a	$1$	$6$	$6$	$6.987$	6.6.1241125.1	$_{}$	None	None	✓	✓	✓		875.2.a.e	$1$	$1$	$-2$	$-5$	$0$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{2}+(-1+\beta _{3}-\beta _{4})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
875.2.a.f	$875$	$2$	875.a	1.a	$1$	$6$	$6$	$6.987$	6.6.3438125.1	$_{}$	None	None	✓	✓	✓		875.2.a.f	$1$	$1$	$-2$	$-3$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
875.2.a.g	$875$	$2$	875.a	1.a	$1$	$6$	$6$	$6.987$	6.6.3438125.1	$_{}$	None	None	✓	✓			875.2.a.f	$1$	$0$	$2$	$3$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(\beta _{3}+\beta _{4})q^{4}+\cdots$
875.2.a.h	$875$	$2$	875.a	1.a	$1$	$6$	$6$	$6.987$	6.6.1241125.1	$_{}$	None	None	✓	✓			875.2.a.e	$1$	$0$	$2$	$5$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+(1-\beta _{3}+\beta _{4})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
875.2.a.i	$875$	$2$	875.a	1.a	$1$	$8$	$8$	$6.987$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		875.2.a.i	$1$	$0$	$-1$	$8$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
875.2.a.j	$875$	$2$	875.a	1.a	$1$	$8$	$8$	$6.987$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		875.2.a.i	$1$	$0$	$1$	$-8$	$0$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-\beta _{4}+\beta _{5})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
875.2.b.a	$875$	$2$	875.b	5.b	$2$	$4$	$4$	$6.987$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			875.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}-2\beta _{3})q^{3}+\cdots$
875.2.b.b	$875$	$2$	875.b	5.b	$2$	$4$	$4$	$6.987$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			875.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$
875.2.b.c	$875$	$2$	875.b	5.b	$2$	$12$	$12$	$6.987$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			875.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}+(-\beta _{5}+\beta _{9}-\beta _{10})q^{3}+\cdots$
875.2.b.d	$875$	$2$	875.b	5.b	$2$	$12$	$12$	$6.987$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			875.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{11})q^{3}+(\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
875.2.b.e	$875$	$2$	875.b	5.b	$2$	$16$	$16$	$6.987$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		875.2.a.i	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(-\beta _{10}+\beta _{13})q^{3}+(-2+\cdots)q^{4}+\cdots$
875.2.e.a	$875$	$2$	875.e	7.c	$3$	$4$	$2$	$6.987$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			875.2.e.a	$2$	$0$	$-3$	$3$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}-\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
875.2.e.b	$875$	$2$	875.e	7.c	$3$	$4$	$2$	$6.987$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			875.2.e.a	$2$	$0$	$3$	$-3$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$
875.2.e.c	$875$	$2$	875.e	7.c	$3$	$24$	$12$	$6.987$		$_{}$	None	None		✓			875.2.e.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
875.2.e.d	$875$	$2$	875.e	7.c	$3$	$28$	$14$	$6.987$		$_{}$	None	None		✓			875.2.e.d	$2$	$0$	$-1$	$-2$	$0$	$-3$			$\mathrm{SU}(2)[C_{3}]$
875.2.e.e	$875$	$2$	875.e	7.c	$3$	$28$	$14$	$6.987$		$_{}$	None	None		✓			875.2.e.d	$2$	$0$	$1$	$2$	$0$	$3$			$\mathrm{SU}(2)[C_{3}]$
875.2.e.f	$875$	$2$	875.e	7.c	$3$	$40$	$20$	$6.987$		$_{}$	None	None		✓	✓		875.2.e.f	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
875.2.f.a	$875$	$2$	875.f	35.f	$4$	$16$	$8$	$6.987$	16.0.$\cdots$.4	$_{}$	$\Q(\sqrt{-35}) $	None		✓			875.2.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$5^{8}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{5}q^{3}-2\beta _{7}q^{4}-\beta _{14}q^{7}+(3\beta _{7}+\cdots)q^{9}+\cdots$
875.2.f.b	$875$	$2$	875.f	35.f	$4$	$16$	$8$	$6.987$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			875.2.f.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+(-\beta _{3}-\beta _{12})q^{3}+(-3\beta _{7}+\cdots)q^{4}+\cdots$
875.2.f.c	$875$	$2$	875.f	35.f	$4$	$32$	$16$	$6.987$		$_{}$	None	None		✓			875.2.f.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
875.2.f.d	$875$	$2$	875.f	35.f	$4$	$64$	$32$	$6.987$		$_{}$	None	None		✓	✓		875.2.f.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
875.2.h.a	$875$	$2$	875.h	25.d	$5$	$4$	$1$	$6.987$	$\Q(\zeta_{10})$	$_{}$	None	None					175.2.h.a	$2$	$0$	$5$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots$
875.2.h.b	$875$	$2$	875.h	25.d	$5$	$28$	$7$	$6.987$		$_{}$	None	None					175.2.h.b	$2$	$0$	$-6$	$-4$	$0$	$28$			$\mathrm{SU}(2)[C_{5}]$
875.2.h.c	$875$	$2$	875.h	25.d	$5$	$32$	$8$	$6.987$		$_{}$	None	None					175.2.h.c	$2$	$0$	$3$	$4$	$0$	$-32$			$\mathrm{SU}(2)[C_{5}]$
875.2.h.d	$875$	$2$	875.h	25.d	$5$	$56$	$14$	$6.987$		$_{}$	None	None					175.2.n.a	$2$	$0$	$-4$	$-4$	$0$	$-56$			$\mathrm{SU}(2)[C_{5}]$
875.2.h.e	$875$	$2$	875.h	25.d	$5$	$56$	$14$	$6.987$		$_{}$	None	None					175.2.n.a	$2$	$0$	$4$	$4$	$0$	$56$			$\mathrm{SU}(2)[C_{5}]$
875.2.k.a	$875$	$2$	875.k	35.j	$6$	$8$	$4$	$6.987$	8.0.12960000.1	$_{}$	None	None		✓			875.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(\beta _{3}-\beta _{6}+\beta _{7})q^{3}+\cdots$
875.2.k.b	$875$	$2$	875.k	35.j	$6$	$24$	$12$	$6.987$		$_{}$	None	None		✓			875.2.e.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
875.2.k.c	$875$	$2$	875.k	35.j	$6$	$40$	$20$	$6.987$		$_{}$	None	None		✓			875.2.e.f	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
875.2.k.d	$875$	$2$	875.k	35.j	$6$	$56$	$28$	$6.987$		$_{}$	None	None		✓	✓		875.2.e.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
875.2.n.a	$875$	$2$	875.n	25.e	$10$	$8$	$2$	$6.987$	$\Q(\zeta_{20})$	$_{}$	None	None					175.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+\cdots$
875.2.n.b	$875$	$2$	875.n	25.e	$10$	$56$	$14$	$6.987$		$_{}$	None	None					175.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
875.2.n.c	$875$	$2$	875.n	25.e	$10$	$56$	$14$	$6.987$		$_{}$	None	None					175.2.n.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
875.2.n.d	$875$	$2$	875.n	25.e	$10$	$64$	$16$	$6.987$		$_{}$	None	None			✓		175.2.h.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
875.2.o.a	$875$	$2$	875.o	35.k	$12$	$128$	$32$	$6.987$		$_{}$	None	None		✓			875.2.o.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
875.2.o.b	$875$	$2$	875.o	35.k	$12$	$128$	$32$	$6.987$		$_{}$	None	None		✓			875.2.o.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
875.2.q.a	$875$	$2$	875.q	175.q	$15$	$144$	$18$	$6.987$		$_{}$	None	None					175.2.q.a	$4$	$0$	$3$	$3$	$0$	$22$			$\mathrm{SU}(2)[C_{15}]$
875.2.q.b	$875$	$2$	875.q	175.q	$15$	$288$	$36$	$6.987$		$_{}$	None	None			✓		175.2.t.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{15}]$
875.2.s.a	$875$	$2$	875.s	175.s	$20$	$144$	$18$	$6.987$		$_{}$	None	None					175.2.s.a	$4$	$0$	$-4$	$0$	$0$	$14$			$\mathrm{SU}(2)[C_{20}]$
875.2.s.b	$875$	$2$	875.s	175.s	$20$	$144$	$18$	$6.987$		$_{}$	None	None					175.2.s.a	$4$	$0$	$4$	$0$	$0$	$-14$			$\mathrm{SU}(2)[C_{20}]$
875.2.s.c	$875$	$2$	875.s	175.s	$20$	$144$	$18$	$6.987$		$_{}$	None	None					175.2.s.a	$4$	$0$	$16$	$0$	$0$	$14$			$\mathrm{SU}(2)[C_{20}]$
875.2.t.a	$875$	$2$	875.t	125.g	$25$	$760$	$38$	$6.987$		$_{}$	None	None		✓			875.2.t.a	$2$	$0$	$0$	$0$	$-5$	$190$			$\mathrm{SU}(2)[C_{25}]$
875.2.t.b	$875$	$2$	875.t	125.g	$25$	$760$	$38$	$6.987$		$_{}$	None	None		✓			875.2.t.b	$2$	$0$	$0$	$0$	$-5$	$-190$			$\mathrm{SU}(2)[C_{25}]$

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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.