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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 82 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
124.1.i.a	$124$	$1$	124.i	124.i	$6$	$4$	$2$	$0.062$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	124.1.i.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
124.2.a.a	$124$	$2$	124.a	1.a	$1$	$1$	$1$	$0.990$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	124.2.a.a	$1$	$1$	$0$	$-2$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-3q^{5}-q^{7}+q^{9}-6q^{11}+\cdots$
124.2.a.b	$124$	$2$	124.a	1.a	$1$	$1$	$1$	$0.990$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	124.2.a.b	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-3q^{9}+6q^{11}-4q^{13}+\cdots$
124.2.d.a	$124$	$2$	124.d	124.d	$2$	$4$	$4$	$0.990$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			124.2.d.a	$4$	$0$	$-4$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+\cdots$
124.2.d.b	$124$	$2$	124.d	124.d	$2$	$4$	$4$	$0.990$	$\Q(\sqrt{6}, \sqrt{-7})$	$_{}$	None	None		✓			124.2.d.b	$4$	$0$	$2$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-2-\beta _{1})q^{4}-2q^{5}+\cdots$
124.2.d.c	$124$	$2$	124.d	124.d	$2$	$6$	$6$	$0.990$	6.0.21717639.1	$_{}$	$\Q(\sqrt{-31}) $	None		✓	✓		124.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{5}q^{2}-\beta _{3}q^{4}+(\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots$
124.2.e.a	$124$	$2$	124.e	31.c	$3$	$6$	$3$	$0.990$	6.0.954288.1	$_{}$	None	None		✓	✓	✓	124.2.e.a	$2$	$0$	$0$	$1$	$-1$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
124.2.f.a	$124$	$2$	124.f	31.d	$5$	$4$	$1$	$0.990$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			124.2.f.a	$2$	$0$	$0$	$-3$	$8$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}^{3})q^{3}+2q^{5}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
124.2.f.b	$124$	$2$	124.f	31.d	$5$	$4$	$1$	$0.990$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			124.2.f.b	$2$	$0$	$0$	$5$	$-6$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots$
124.2.g.a	$124$	$2$	124.g	124.g	$6$	$28$	$14$	$0.990$		$_{}$	None	None		✓	✓	✓	124.2.g.a	$4$	$0$	$-4$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
124.2.j.a	$124$	$2$	124.j	124.j	$10$	$8$	$2$	$0.990$	$\Q(\zeta_{20})$	$_{}$	None	None		✓			124.2.j.a	$4$	$0$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots$
124.2.j.b	$124$	$2$	124.j	124.j	$10$	$48$	$12$	$0.990$		$_{}$	None	None		✓	✓		124.2.j.b	$4$	$0$	$-1$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{10}]$
124.2.m.a	$124$	$2$	124.m	31.g	$15$	$24$	$3$	$0.990$		$_{}$	None	None		✓	✓	✓	124.2.m.a	$2$	$0$	$0$	$-1$	$1$	$-9$			$\mathrm{SU}(2)[C_{15}]$
124.2.p.a	$124$	$2$	124.p	124.p	$30$	$112$	$14$	$0.990$		$_{}$	None	None		✓	✓	✓	124.2.p.a	$4$	$0$	$-6$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{30}]$
124.3.b.a	$124$	$3$	124.b	4.b	$2$	$30$	$30$	$3.379$		$_{}$	None	None		✓	✓	✓	124.3.b.a	$2$	$0$	$-2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
124.3.c.a	$124$	$3$	124.c	31.b	$2$	$2$	$2$	$3.379$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			124.3.c.a	$2$	$0$	$0$	$0$	$-12$	$-20$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-6 q^{5}-10 q^{7}-3 q^{9}+5\beta q^{11}+\cdots$
124.3.c.b	$124$	$3$	124.c	31.b	$2$	$4$	$4$	$3.379$	4.0.63368.1	$_{}$	None	None		✓	✓		124.3.c.b	$2$	$0$	$0$	$0$	$18$	$6$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(4+\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots$
124.3.h.a	$124$	$3$	124.h	31.e	$6$	$10$	$5$	$3.379$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓	✓	124.3.h.a	$2$	$0$	$0$	$3$	$3$	$1$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{3}+(-\beta _{1}-\beta _{6})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
124.3.i.a	$124$	$3$	124.i	124.i	$6$	$60$	$30$	$3.379$		$_{}$	None	None		✓	✓	✓	124.3.i.a	$4$	$0$	$-4$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
124.3.k.a	$124$	$3$	124.k	31.f	$10$	$24$	$6$	$3.379$		$_{}$	None	None		✓	✓	✓	124.3.k.a	$2$	$0$	$0$	$0$	$-6$	$-6$			$\mathrm{SU}(2)[C_{10}]$
124.3.l.a	$124$	$3$	124.l	124.l	$10$	$120$	$30$	$3.379$		$_{}$	None	None		✓	✓	✓	124.3.l.a	$4$	$0$	$-3$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{10}]$
124.3.n.a	$124$	$3$	124.n	124.n	$30$	$240$	$30$	$3.379$		$_{}$	None	None		✓	✓	✓	124.3.n.a	$4$	$0$	$-6$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{30}]$
124.3.o.a	$124$	$3$	124.o	31.h	$30$	$40$	$5$	$3.379$		$_{}$	None	None		✓	✓	✓	124.3.o.a	$2$	$0$	$0$	$-3$	$-3$	$19$			$\mathrm{SU}(2)[C_{30}]$
124.4.a.a	$124$	$4$	124.a	1.a	$1$	$4$	$4$	$7.316$	4.4.841724.1	$_{}$	None	None	✓	✓	✓	✓	124.4.a.a	$1$	$1$	$0$	$-4$	$-14$	$-12$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{3}+(-3-\beta _{1}-\beta _{2}+2\beta _{3})q^{5}+\cdots$
124.4.a.b	$124$	$4$	124.a	1.a	$1$	$4$	$4$	$7.316$	4.4.4000044.1	$_{}$	None	None	✓	✓	✓	✓	124.4.a.b	$1$	$0$	$0$	$2$	$6$	$16$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots$
124.4.d.a	$124$	$4$	124.d	124.d	$2$	$2$	$2$	$7.316$	$\Q(\sqrt{-31}) $	$_{}$	$\Q(\sqrt{-31}) $	None		✓			124.4.d.a	$4$	$0$	$1$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+(-8+\beta )q^{4}-2q^{5}+(6-12\beta )q^{7}+\cdots$
124.4.d.b	$124$	$4$	124.d	124.d	$2$	$4$	$4$	$7.316$	$\Q(\sqrt{-3}, \sqrt{-31})$	$_{}$	$\Q(\sqrt{-31}) $	None		✓			124.4.d.b	$4$	$0$	$-1$	$0$	$4$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-\beta _{1}-\beta _{3})q^{2}+(4+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
124.4.d.c	$124$	$4$	124.d	124.d	$2$	$40$	$40$	$7.316$		$_{}$	None	None		✓	✓		124.4.d.c	$4$	$0$	$-2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
124.4.e.a	$124$	$4$	124.e	31.c	$3$	$2$	$1$	$7.316$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			124.4.e.a	$2$	$0$	$0$	$5$	$15$	$-29$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(5-5\zeta_{6})q^{3}+15\zeta_{6}q^{5}+(-29+29\zeta_{6})q^{7}+\cdots$
124.4.e.b	$124$	$4$	124.e	31.c	$3$	$6$	$3$	$7.316$	6.0.$\cdots$.1	$_{}$	None	None		✓			124.4.e.b	$2$	$0$	$0$	$-9$	$-3$	$45$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3-\beta _{1}-\beta _{2}+3\beta _{3})q^{3}+(2\beta _{1}+\cdots)q^{5}+\cdots$
124.4.e.c	$124$	$4$	124.e	31.c	$3$	$8$	$4$	$7.316$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓	✓		124.4.e.c	$2$	$0$	$0$	$0$	$-16$	$-32$		$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{3}+(-\beta _{3}-4\beta _{4}-\beta _{6}+\beta _{7})q^{5}+\cdots$
124.4.f.a	$124$	$4$	124.f	31.d	$5$	$32$	$8$	$7.316$		$_{}$	None	None		✓	✓	✓	124.4.f.a	$2$	$0$	$0$	$2$	$8$	$-34$			$\mathrm{SU}(2)[C_{5}]$
124.4.g.a	$124$	$4$	124.g	124.g	$6$	$92$	$46$	$7.316$		$_{}$	None	None		✓	✓	✓	124.4.g.a	$4$	$0$	$-4$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
124.4.j.a	$124$	$4$	124.j	124.j	$10$	$184$	$46$	$7.316$		$_{}$	None	None		✓	✓	✓	124.4.j.a	$4$	$0$	$-3$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{10}]$
124.4.m.a	$124$	$4$	124.m	31.g	$15$	$64$	$8$	$7.316$		$_{}$	None	None		✓	✓	✓	124.4.m.a	$2$	$0$	$0$	$4$	$4$	$46$			$\mathrm{SU}(2)[C_{15}]$
124.4.p.a	$124$	$4$	124.p	124.p	$30$	$368$	$46$	$7.316$		$_{}$	None	None		✓	✓	✓	124.4.p.a	$4$	$0$	$-6$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{30}]$
124.5.b.a	$124$	$5$	124.b	4.b	$2$	$60$	$60$	$12.818$		$_{}$	None	None		✓	✓	✓	124.5.b.a	$2$	$0$	$6$	$0$	$24$	$0$			$\mathrm{SU}(2)[C_{2}]$
124.5.c.a	$124$	$5$	124.c	31.b	$2$	$10$	$10$	$12.818$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓	✓	✓	124.5.c.a	$2$	$0$	$0$	$0$	$-6$	$-2$		$2^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}-\beta _{4}q^{7}+(-15+\cdots)q^{9}+\cdots$
124.5.h.a	$124$	$5$	124.h	31.e	$6$	$22$	$11$	$12.818$		$_{}$	None	None		✓	✓	✓	124.5.h.a	$2$	$0$	$0$	$9$	$-3$	$15$			$\mathrm{SU}(2)[C_{6}]$
124.5.i.a	$124$	$5$	124.i	124.i	$6$	$124$	$62$	$12.818$		$_{}$	None	None		✓	✓	✓	124.5.i.a	$4$	$0$	$-4$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
124.5.k.a	$124$	$5$	124.k	31.f	$10$	$40$	$10$	$12.818$		$_{}$	None	None		✓	✓	✓	124.5.k.a	$2$	$0$	$0$	$0$	$6$	$202$			$\mathrm{SU}(2)[C_{10}]$
124.5.l.a	$124$	$5$	124.l	124.l	$10$	$248$	$62$	$12.818$		$_{}$	None	None		✓	✓	✓	124.5.l.a	$4$	$0$	$-3$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{10}]$
124.5.n.a	$124$	$5$	124.n	124.n	$30$	$496$	$62$	$12.818$		$_{}$	None	None		✓	✓	✓	124.5.n.a	$4$	$0$	$-6$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{30}]$
124.5.o.a	$124$	$5$	124.o	31.h	$30$	$88$	$11$	$12.818$		$_{}$	None	None		✓	✓	✓	124.5.o.a	$2$	$0$	$0$	$-9$	$3$	$-215$			$\mathrm{SU}(2)[C_{30}]$
124.6.a.a	$124$	$6$	124.a	1.a	$1$	$6$	$6$	$19.888$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	124.6.a.a	$1$	$1$	$0$	$2$	$-75$	$-157$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-12+\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots$
124.6.a.b	$124$	$6$	124.a	1.a	$1$	$6$	$6$	$19.888$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	124.6.a.b	$1$	$0$	$0$	$20$	$25$	$39$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(3+\beta _{1})q^{3}+(4+\beta _{1}-\beta _{5})q^{5}+(6+\cdots)q^{7}+\cdots$
124.6.d.a	$124$	$6$	124.d	124.d	$2$	$6$	$6$	$19.888$	6.0.21717639.1	$_{}$	$\Q(\sqrt{-31}) $	None		✓			124.6.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}+\beta _{2}+2\beta _{4}-2\beta _{5})q^{2}+(-4\beta _{1}+\cdots)q^{4}+\cdots$
124.6.d.b	$124$	$6$	124.d	124.d	$2$	$72$	$72$	$19.888$		$_{}$	None	None		✓	✓		124.6.d.b	$4$	$0$	$-2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
124.6.e.a	$124$	$6$	124.e	31.c	$3$	$26$	$13$	$19.888$		$_{}$	None	None		✓	✓	✓	124.6.e.a	$2$	$0$	$0$	$-7$	$29$	$-85$			$\mathrm{SU}(2)[C_{3}]$
124.6.f.a	$124$	$6$	124.f	31.d	$5$	$56$	$14$	$19.888$		$_{}$	None	None		✓	✓	✓	124.6.f.a	$2$	$0$	$0$	$2$	$-58$	$104$			$\mathrm{SU}(2)[C_{5}]$

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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.