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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 62 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
237.1.k.a	$237$	$1$	237.k	237.k	$26$	$12$	$1$	$0.118$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q+\zeta_{26}^{2}q^{3}-\zeta_{26}^{3}q^{4}+(\zeta_{26}^{8}-\zeta_{26}^{9}+\cdots)q^{7}+\cdots$
237.2.a.a	$237$	$2$	237.a	1.a	$1$	$2$	$2$	$1.892$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
237.2.a.b	$237$	$2$	237.a	1.a	$1$	$4$	$4$	$1.892$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-4$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
237.2.a.c	$237$	$2$	237.a	1.a	$1$	$7$	$7$	$1.892$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$7$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
237.2.b.a	$237$	$2$	237.b	237.b	$2$	$24$	$24$	$1.892$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
237.2.e.a	$237$	$2$	237.e	79.c	$3$	$12$	$6$	$1.892$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$6$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}+\beta _{4})q^{2}+(1+\beta _{4})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
237.2.e.b	$237$	$2$	237.e	79.c	$3$	$14$	$7$	$1.892$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$-7$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{7})q^{3}+(-\beta _{4}-\beta _{7}+\cdots)q^{4}+\cdots$
237.2.h.a	$237$	$2$	237.h	237.h	$6$	$2$	$1$	$1.892$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$1$	$0$	$-3$	$0$	$-6$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{7}+\cdots$
237.2.h.b	$237$	$2$	237.h	237.h	$6$	$48$	$24$	$1.892$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{6}]$
237.2.i.a	$237$	$2$	237.i	79.e	$13$	$72$	$6$	$1.892$		$_{}$	None	None		$2$	$0$	$1$	$6$	$-9$	$0$			$\mathrm{SU}(2)[C_{13}]$
237.2.i.b	$237$	$2$	237.i	79.e	$13$	$96$	$8$	$1.892$		$_{}$	None	None		$2$	$0$	$-5$	$-8$	$9$	$-12$			$\mathrm{SU}(2)[C_{13}]$
237.2.l.a	$237$	$2$	237.l	237.l	$26$	$288$	$24$	$1.892$		$_{}$	None	None		$4$	$0$	$0$	$-13$	$0$	$-26$			$\mathrm{SU}(2)[C_{26}]$
237.2.m.a	$237$	$2$	237.m	79.g	$39$	$144$	$6$	$1.892$		$_{}$	None	None		$2$	$0$	$-4$	$-6$	$12$	$0$			$\mathrm{SU}(2)[C_{39}]$
237.2.m.b	$237$	$2$	237.m	79.g	$39$	$168$	$7$	$1.892$		$_{}$	None	None		$2$	$0$	$2$	$7$	$-12$	$4$			$\mathrm{SU}(2)[C_{39}]$
237.2.n.a	$237$	$2$	237.n	237.n	$78$	$24$	$1$	$1.892$		$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$6$			$\mathrm{U}(1)[D_{78}]$
237.2.n.b	$237$	$2$	237.n	237.n	$78$	$576$	$24$	$1.892$		$_{}$	None	None		$4$	$0$	$0$	$-26$	$0$	$-40$			$\mathrm{SU}(2)[C_{78}]$
237.3.c.a	$237$	$3$	237.c	3.b	$2$	$52$	$52$	$6.458$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
237.3.d.a	$237$	$3$	237.d	79.b	$2$	$26$	$26$	$6.458$		$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
237.3.f.a	$237$	$3$	237.f	79.d	$6$	$26$	$13$	$6.458$		$_{}$	None	None		$2$	$0$	$1$	$39$	$6$	$21$			$\mathrm{SU}(2)[C_{6}]$
237.3.f.b	$237$	$3$	237.f	79.d	$6$	$28$	$14$	$6.458$		$_{}$	None	None		$2$	$0$	$1$	$-42$	$-6$	$-15$			$\mathrm{SU}(2)[C_{6}]$
237.3.g.a	$237$	$3$	237.g	237.g	$6$	$2$	$1$	$6.458$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+3\zeta_{6}q^{3}+(-4+4\zeta_{6})q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
237.3.g.b	$237$	$3$	237.g	237.g	$6$	$100$	$50$	$6.458$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-14$			$\mathrm{SU}(2)[C_{6}]$
237.3.j.a	$237$	$3$	237.j	79.f	$26$	$312$	$26$	$6.458$		$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{26}]$
237.3.k.a	$237$	$3$	237.k	237.k	$26$	$624$	$52$	$6.458$		$_{}$	None	None		$4$	$0$	$0$	$-11$	$0$	$-26$			$\mathrm{SU}(2)[C_{26}]$
237.3.o.a	$237$	$3$	237.o	237.o	$78$	$24$	$1$	$6.458$		$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-3$	$0$	$2$			$\mathrm{U}(1)[D_{78}]$
237.3.o.b	$237$	$3$	237.o	237.o	$78$	$1200$	$50$	$6.458$		$_{}$	None	None		$4$	$0$	$0$	$-22$	$0$	$-38$			$\mathrm{SU}(2)[C_{78}]$
237.3.p.a	$237$	$3$	237.p	79.h	$78$	$312$	$13$	$6.458$		$_{}$	None	None		$2$	$0$	$-1$	$-39$	$72$	$-21$			$\mathrm{SU}(2)[C_{78}]$
237.3.p.b	$237$	$3$	237.p	79.h	$78$	$336$	$14$	$6.458$		$_{}$	None	None		$2$	$0$	$-1$	$42$	$-72$	$15$			$\mathrm{SU}(2)[C_{78}]$
237.4.a.a	$237$	$4$	237.a	1.a	$1$	$6$	$6$	$13.983$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$18$	$-8$	$-37$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+3q^{3}+(1-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
237.4.a.b	$237$	$4$	237.a	1.a	$1$	$9$	$9$	$13.983$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$-27$	$8$	$5$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots$
237.4.a.c	$237$	$4$	237.a	1.a	$1$	$11$	$11$	$13.983$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$-33$	$-12$	$-23$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
237.4.a.d	$237$	$4$	237.a	1.a	$1$	$14$	$14$	$13.983$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$42$	$12$	$47$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots$
237.4.b.a	$237$	$4$	237.b	237.b	$2$	$2$	$2$	$13.983$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{6}q^{3}+8q^{4}-6\zeta_{6}q^{7}-3^{3}q^{9}+\cdots$
237.4.b.b	$237$	$4$	237.b	237.b	$2$	$76$	$76$	$13.983$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
237.4.e.a	$237$	$4$	237.e	79.c	$3$	$38$	$19$	$13.983$		$_{}$	None	None		$2$	$0$	$-1$	$-57$	$17$	$-17$			$\mathrm{SU}(2)[C_{3}]$
237.4.e.b	$237$	$4$	237.e	79.c	$3$	$42$	$21$	$13.983$		$_{}$	None	None		$2$	$0$	$-1$	$63$	$-17$	$19$			$\mathrm{SU}(2)[C_{3}]$
237.4.h.a	$237$	$4$	237.h	237.h	$6$	$156$	$78$	$13.983$		$_{}$	None	None		$4$	$0$	$0$	$-3$	$0$	$72$			$\mathrm{SU}(2)[C_{6}]$
237.4.i.a	$237$	$4$	237.i	79.e	$13$	$240$	$20$	$13.983$		$_{}$	None	None		$2$	$0$	$2$	$-60$	$87$	$-10$			$\mathrm{SU}(2)[C_{13}]$
237.4.i.b	$237$	$4$	237.i	79.e	$13$	$240$	$20$	$13.983$		$_{}$	None	None		$2$	$0$	$2$	$60$	$-87$	$18$			$\mathrm{SU}(2)[C_{13}]$
237.4.l.a	$237$	$4$	237.l	237.l	$26$	$24$	$2$	$13.983$		$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{26}]$
237.4.l.b	$237$	$4$	237.l	237.l	$26$	$912$	$76$	$13.983$		$_{}$	None	None		$4$	$0$	$0$	$-13$	$0$	$-26$			$\mathrm{SU}(2)[C_{26}]$
237.4.m.a	$237$	$4$	237.m	79.g	$39$	$456$	$19$	$13.983$		$_{}$	None	None		$2$	$0$	$1$	$57$	$-108$	$17$			$\mathrm{SU}(2)[C_{39}]$
237.4.m.b	$237$	$4$	237.m	79.g	$39$	$504$	$21$	$13.983$		$_{}$	None	None		$2$	$0$	$1$	$-63$	$108$	$-19$			$\mathrm{SU}(2)[C_{39}]$
237.4.n.a	$237$	$4$	237.n	237.n	$78$	$1872$	$78$	$13.983$		$_{}$	None	None		$4$	$0$	$0$	$-23$	$0$	$-124$			$\mathrm{SU}(2)[C_{78}]$
237.5.d.a	$237$	$5$	237.d	79.b	$2$	$54$	$54$	$24.499$		$_{}$	None	None		$2$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
237.6.a.a	$237$	$6$	237.a	1.a	$1$	$12$	$12$	$38.011$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-8$	$108$	$-42$	$-284$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+9q^{3}+(8-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
237.6.a.b	$237$	$6$	237.a	1.a	$1$	$15$	$15$	$38.011$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$12$	$-135$	$36$	$206$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-9q^{3}+(2^{4}-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
237.6.a.c	$237$	$6$	237.a	1.a	$1$	$17$	$17$	$38.011$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-8$	$-153$	$-64$	$10$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-9q^{3}+(15+\beta _{1}+\beta _{2})q^{4}+\cdots$
237.6.a.d	$237$	$6$	237.a	1.a	$1$	$20$	$20$	$38.011$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$12$	$180$	$58$	$304$	$-$	$2^{7}\cdot 5$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+9q^{3}+(20-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
237.7.d.a	$237$	$7$	237.d	79.b	$2$	$80$	$80$	$54.523$		$_{}$	None	None		$2$	$0$	$20$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.