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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 (1-50 of 743 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
61.2.c.a	$61$	$2$	61.c	61.c	$3$	$8$	$4$	$0.487$	8.0.310217769.2	None		$2$	$0$	$0$	$-6$	$-2$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
73.2.c.a	$73$	$2$	73.c	73.c	$3$	$8$	$4$	$0.583$	8.0.142635249.1	None		$2$	$0$	$1$	$-6$	$2$	$2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots$
91.2.f.c	$91$	$2$	91.f	13.c	$3$	$8$	$4$	$0.727$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$1$	$-1$	$-14$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
95.2.e.c	$95$	$2$	95.e	19.c	$3$	$8$	$4$	$0.759$	8.0.4601315889.1	None		$2$	$0$	$-1$	$-3$	$-4$	$-8$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
99.2.e.e	$99$	$2$	99.e	9.c	$3$	$8$	$4$	$0.791$	8.0.508277025.1	None		$2$	$0$	$-1$	$5$	$-4$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{2}-\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots$
153.2.e.b	$153$	$2$	153.e	9.c	$3$	$8$	$4$	$1.222$	8.0.152695449.1	None		$2$	$0$	$1$	$-1$	$-1$	$3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3}-\beta _{6})q^{2}+(-\beta _{1}+\beta _{6})q^{3}+\cdots$
155.2.e.c	$155$	$2$	155.e	31.c	$3$	$8$	$4$	$1.238$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-2$	$3$	$4$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{2}+(\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
155.2.e.d	$155$	$2$	155.e	31.c	$3$	$8$	$4$	$1.238$	8.0.42575625.1	None		$2$	$0$	$2$	$-1$	$-4$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4}+\beta _{7})q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
171.2.f.c	$171$	$2$	171.f	19.c	$3$	$8$	$4$	$1.365$	8.0.764411904.5	None		$4$	$0$	$0$	$0$	$0$	$-8$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{2}+(-1-\beta _{3}+\beta _{4}-\beta _{6})q^{4}+\cdots$
172.2.e.a	$172$	$2$	172.e	43.c	$3$	$8$	$4$	$1.373$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$-3$	$0$	$2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{5}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$
9.6.c.a	$9$	$6$	9.c	9.c	$3$	$8$	$4$	$1.443$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$3$	$-12$	$78$	$28$	$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots$
182.2.f.c	$182$	$2$	182.f	7.c	$3$	$8$	$4$	$1.453$	8.0.8681953329.1	None		$2$	$0$	$-4$	$0$	$-2$	$7$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
194.2.c.c	$194$	$2$	194.c	97.c	$3$	$8$	$4$	$1.549$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-4$	$1$	$5$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
206.2.c.c	$206$	$2$	206.c	103.c	$3$	$8$	$4$	$1.645$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-4$	$-2$	$-6$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{2}-\beta _{2}q^{3}-\beta _{4}q^{4}+(1+\cdots)q^{5}+\cdots$
225.2.e.c	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	8.0.1223810289.2	None		$2$	$0$	$-2$	$1$	$0$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
225.2.e.d	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{24}^{7}q^{2}+(\zeta_{24}^{6}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
225.2.e.e	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	8.0.1223810289.2	None		$2$	$0$	$2$	$-1$	$0$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{4}-\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
231.2.i.e	$231$	$2$	231.i	7.c	$3$	$8$	$4$	$1.845$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-2$	$-4$	$-4$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
234.2.e.e	$234$	$2$	234.e	9.c	$3$	$8$	$4$	$1.868$	8.0.508277025.1	None		$2$	$0$	$-4$	$3$	$-2$	$-4$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{7})q^{2}+(-\beta _{3}+\beta _{4})q^{3}-\beta _{7}q^{4}+\cdots$
244.2.e.c	$244$	$2$	244.e	61.c	$3$	$8$	$4$	$1.948$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$6$	$2$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
254.2.c.c	$254$	$2$	254.c	127.c	$3$	$8$	$4$	$2.028$	8.0.6498455769.2	None		$2$	$0$	$8$	$-2$	$2$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+\beta _{6}q^{3}+q^{4}+(1+2\beta _{4}-\beta _{7})q^{5}+\cdots$
13.6.c.a	$13$	$6$	13.c	13.c	$3$	$8$	$4$	$2.085$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-5$	$8$	$-20$	$68$	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}+\beta _{3})q^{2}+(2-2\beta _{3}-\beta _{5}+\cdots)q^{3}+\cdots$
266.2.f.d	$266$	$2$	266.f	19.c	$3$	$8$	$4$	$2.124$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$4$	$1$	$-1$	$8$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}+(-\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{4}+\cdots$
273.2.i.d	$273$	$2$	273.i	7.c	$3$	$8$	$4$	$2.180$	8.0.4868829729.1	None		$2$	$0$	$1$	$-4$	$-3$	$9$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots$
7.8.c.a	$7$	$8$	7.c	7.c	$3$	$8$	$4$	$2.187$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$6$	$-28$	$-252$	$672$	$2^{8}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(-6+\cdots)q^{3}+\cdots$
278.2.c.b	$278$	$2$	278.c	139.c	$3$	$8$	$4$	$2.220$	8.0.592240896.6	None		$2$	$0$	$4$	$0$	$4$	$2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$
279.2.h.e	$279$	$2$	279.h	31.c	$3$	$8$	$4$	$2.228$	8.0.207360000.1	None		$4$	$0$	$0$	$0$	$0$	$-4$	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}+\beta _{7}q^{5}+(-1+\cdots)q^{7}+\cdots$
288.2.i.f	$288$	$2$	288.i	9.c	$3$	$8$	$4$	$2.300$	8.0.170772624.1	None		$4$	$0$	$0$	$0$	$2$	$0$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{3}+(1-\beta _{4}+\beta _{7})q^{5}+\cdots$
39.4.e.c	$39$	$4$	39.e	13.c	$3$	$8$	$4$	$2.301$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-2$	$12$	$-12$	$14$	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(3+3\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
291.2.e.e	$291$	$2$	291.e	97.c	$3$	$8$	$4$	$2.324$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$1$	$4$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-2-\beta _{4}+2\beta _{5}+\cdots)q^{4}+\cdots$
297.2.e.e	$297$	$2$	297.e	9.c	$3$	$8$	$4$	$2.372$	8.0.508277025.1	None		$2$	$0$	$1$	$0$	$4$	$-1$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{3}+3\beta _{5})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
299.2.e.b	$299$	$2$	299.e	13.c	$3$	$8$	$4$	$2.388$	8.0.1658525625.6	None		$2$	$0$	$-1$	$-2$	$4$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
302.2.c.b	$302$	$2$	302.c	151.c	$3$	$8$	$4$	$2.411$	8.0.2654825625.1	None		$2$	$0$	$4$	$2$	$3$	$5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3})q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
305.2.e.d	$305$	$2$	305.e	61.c	$3$	$8$	$4$	$2.435$	8.0.624650049.1	None		$2$	$0$	$2$	$-2$	$4$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2}+\beta _{4})q^{2}+(-1+\beta _{6}-\beta _{7})q^{3}+\cdots$
306.2.e.f	$306$	$2$	306.e	9.c	$3$	$8$	$4$	$2.443$	8.0.5206055409.1	None		$2$	$0$	$4$	$-3$	$-1$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
315.2.i.c	$315$	$2$	315.i	9.c	$3$	$8$	$4$	$2.515$	8.0.142635249.1	None		$2$	$0$	$1$	$-1$	$-4$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\beta _{6})q^{3}+\cdots$
315.2.i.d	$315$	$2$	315.i	9.c	$3$	$8$	$4$	$2.515$	$\Q(\zeta_{15})$	None		$2$	$0$	$1$	$3$	$4$	$4$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\zeta_{15}-\zeta_{15}^{2}+\zeta_{15}^{3})q^{2}+(1+\cdots)q^{3}+\cdots$
322.2.e.a	$322$	$2$	322.e	7.c	$3$	$8$	$4$	$2.571$	8.0.310217769.2	None		$2$	$0$	$-4$	$-3$	$-7$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{5})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots$
322.2.e.b	$322$	$2$	322.e	7.c	$3$	$8$	$4$	$2.571$	8.0.1767277521.3	None		$2$	$0$	$-4$	$5$	$5$	$1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots$
322.2.e.c	$322$	$2$	322.e	7.c	$3$	$8$	$4$	$2.571$	8.0.1767277521.3	None		$2$	$0$	$4$	$-1$	$-3$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{6})q^{2}+(\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7})q^{3}+\cdots$
322.2.e.d	$322$	$2$	322.e	7.c	$3$	$8$	$4$	$2.571$	8.0.6498455769.2	None		$2$	$0$	$4$	$-1$	$5$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{5})q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
344.2.i.c	$344$	$2$	344.i	43.c	$3$	$8$	$4$	$2.747$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$1$	$0$	$4$	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\beta _{2}q^{7}+\cdots$
357.2.i.d	$357$	$2$	357.i	7.c	$3$	$8$	$4$	$2.851$	8.0.1767277521.3	None		$2$	$0$	$1$	$-4$	$-4$	$7$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}+\beta _{7})q^{2}-\beta _{6}q^{3}+(\beta _{4}+\beta _{5}-2\beta _{6}+\cdots)q^{4}+\cdots$
357.2.i.e	$357$	$2$	357.i	7.c	$3$	$8$	$4$	$2.851$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$3$	$-4$	$6$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}+\beta _{4})q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
360.2.q.e	$360$	$2$	360.q	9.c	$3$	$8$	$4$	$2.875$	8.0.856615824.2	None		$2$	$0$	$0$	$0$	$-4$	$1$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots$
361.2.c.j	$361$	$2$	361.c	19.c	$3$	$8$	$4$	$2.883$	8.0.324000000.2	None		$4$	$0$	$0$	$0$	$4$	$-16$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}-\beta _{3}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots$
49.4.c.e	$49$	$4$	49.c	7.c	$3$	$8$	$4$	$2.891$	8.0.$\cdots$.19	None		$4$	$0$	$-2$	$0$	$0$	$0$	$7^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2}-\beta _{6})q^{2}+\beta _{3}q^{3}+(-8+\cdots)q^{4}+\cdots$
364.2.j.e	$364$	$2$	364.j	7.c	$3$	$8$	$4$	$2.907$	8.0.856615824.2	None		$2$	$0$	$0$	$-3$	$1$	$1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
380.2.i.c	$380$	$2$	380.i	19.c	$3$	$8$	$4$	$3.034$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$-1$	$-4$	$0$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$
385.2.i.a	$385$	$2$	385.i	7.c	$3$	$8$	$4$	$3.074$	8.0.310217769.2	None		$2$	$0$	$3$	$3$	$-4$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2}-\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots$

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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.