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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 (37 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
2416.1.e.a	$2416$	$1$	2416.e	151.b	$2$	$3$	$3$	$1.206$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓		✓	✓	151.1.b.a	$2$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+\beta _{2}q^{5}+q^{9}+\beta _{1}q^{11}-\beta _{1}q^{17}+\cdots$
2416.1.m.a	$2416$	$1$	2416.m	2416.m	$4$	$2$	$1$	$1.206$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-151}) $	None		✓			2416.1.m.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$
2416.1.m.b	$2416$	$1$	2416.m	2416.m	$4$	$12$	$6$	$1.206$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-151}) $	None		✓	✓		2416.1.m.b	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{28}^{13}q^{2}-\zeta_{28}^{12}q^{4}+(\zeta_{28}^{10}+\cdots)q^{5}+\cdots$
2416.1.p.a	$2416$	$1$	2416.p	604.h	$6$	$8$	$4$	$1.206$	8.0.12960000.1	$A_{5}$	None	None		✓	✓	✓	2416.1.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{7}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots$
2416.2.a.a	$2416$	$2$	2416.a	1.a	$1$	$1$	$1$	$19.292$	$\Q$	$_{}$	None	None	✓				302.2.a.a	$1$	$0$	$0$	$-2$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
2416.2.a.b	$2416$	$2$	2416.a	1.a	$1$	$1$	$1$	$19.292$	$\Q$	$_{}$	None	None	✓				302.2.a.c	$1$	$0$	$0$	$1$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+2q^{7}-2q^{9}-2q^{11}+\cdots$
2416.2.a.c	$2416$	$2$	2416.a	1.a	$1$	$1$	$1$	$19.292$	$\Q$	$_{}$	None	None	✓				1208.2.a.a	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}+2q^{11}+2q^{13}+\cdots$
2416.2.a.d	$2416$	$2$	2416.a	1.a	$1$	$1$	$1$	$19.292$	$\Q$	$_{}$	None	None	✓				302.2.a.b	$1$	$0$	$0$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{7}+6q^{9}+6q^{11}-2q^{13}+\cdots$
2416.2.a.e	$2416$	$2$	2416.a	1.a	$1$	$2$	$2$	$19.292$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				302.2.a.d	$1$	$1$	$0$	$2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2-2\beta )q^{7}+2\beta q^{9}+(-2+\cdots)q^{11}+\cdots$
2416.2.a.f	$2416$	$2$	2416.a	1.a	$1$	$3$	$3$	$19.292$	3.3.257.1	$_{}$	None	None	✓				151.2.a.b	$1$	$0$	$0$	$-6$	$5$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+(2-\beta _{1}-\beta _{2})q^{5}+2q^{7}+q^{9}+\cdots$
2416.2.a.g	$2416$	$2$	2416.a	1.a	$1$	$3$	$3$	$19.292$	3.3.473.1	$_{}$	None	None	✓				604.2.a.b	$1$	$0$	$0$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}-2\beta _{1}q^{7}-3q^{9}+(2+\cdots)q^{11}+\cdots$
2416.2.a.h	$2416$	$2$	2416.a	1.a	$1$	$3$	$3$	$19.292$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				151.2.a.a	$1$	$1$	$0$	$1$	$-7$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-3+\beta _{1}-\beta _{2})q^{5}+q^{7}+\cdots$
2416.2.a.i	$2416$	$2$	2416.a	1.a	$1$	$3$	$3$	$19.292$	3.3.321.1	$_{}$	None	None	✓				1208.2.a.b	$1$	$1$	$0$	$1$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots$
2416.2.a.j	$2416$	$2$	2416.a	1.a	$1$	$3$	$3$	$19.292$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				604.2.a.a	$1$	$0$	$0$	$3$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+2\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1}-2\beta _{2})q^{5}+\cdots$
2416.2.a.k	$2416$	$2$	2416.a	1.a	$1$	$4$	$4$	$19.292$	4.4.6224.1	$_{}$	None	None	✓				302.2.a.f	$1$	$1$	$0$	$-2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
2416.2.a.l	$2416$	$2$	2416.a	1.a	$1$	$4$	$4$	$19.292$	4.4.2777.1	$_{}$	None	None	✓				1208.2.a.c	$1$	$1$	$0$	$-1$	$-7$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{1})q^{5}+2\beta _{3}q^{7}+\cdots$
2416.2.a.m	$2416$	$2$	2416.a	1.a	$1$	$4$	$4$	$19.292$	4.4.25808.1	$_{}$	None	None	✓				302.2.a.e	$1$	$0$	$0$	$0$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$
2416.2.a.n	$2416$	$2$	2416.a	1.a	$1$	$6$	$6$	$19.292$	6.6.12253129.1	$_{}$	None	None	✓		✓		604.2.a.c	$1$	$1$	$0$	$-3$	$6$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{4})q^{3}+(1+\beta _{1}+\beta _{5})q^{5}+\cdots$
2416.2.a.o	$2416$	$2$	2416.a	1.a	$1$	$6$	$6$	$19.292$	6.6.4838537.1	$_{}$	None	None	✓		✓		151.2.a.c	$1$	$0$	$0$	$5$	$6$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+(1+\beta _{4})q^{5}+\cdots$
2416.2.a.p	$2416$	$2$	2416.a	1.a	$1$	$8$	$8$	$19.292$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				1208.2.a.d	$1$	$0$	$0$	$5$	$6$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-\beta _{4}-\beta _{6})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
2416.2.a.q	$2416$	$2$	2416.a	1.a	$1$	$11$	$11$	$19.292$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓		✓		1208.2.a.f	$1$	$1$	$0$	$-5$	$-8$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{3}+\beta _{7}+\cdots)q^{7}+\cdots$
2416.2.a.r	$2416$	$2$	2416.a	1.a	$1$	$11$	$11$	$19.292$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓		✓		1208.2.a.e	$1$	$0$	$0$	$-3$	$12$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}+\beta _{8}q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots$
2416.2.h.a	$2416$	$2$	2416.h	604.d	$2$	$24$	$24$	$19.292$		$_{}$	None	None		✓			2416.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2416.2.h.b	$2416$	$2$	2416.h	604.d	$2$	$52$	$52$	$19.292$		$_{}$	None	None		✓	✓		2416.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2416.4.a.a	$2416$	$4$	2416.a	1.a	$1$	$1$	$1$	$142.549$	$\Q$	$_{}$	None	None	✓				1208.4.a.a	$1$	$0$	$0$	$7$	$12$	$22$	$+$	$1$	$\mathrm{SU}(2)$	$q+7q^{3}+12q^{5}+22q^{7}+22q^{9}+2q^{11}+\cdots$
2416.4.a.b	$2416$	$4$	2416.a	1.a	$1$	$8$	$8$	$142.549$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				302.4.a.a	$1$	$1$	$0$	$3$	$2$	$25$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(1-\beta _{5}+\beta _{6}+\beta _{7})q^{5}+(3+\cdots)q^{7}+\cdots$
2416.4.a.c	$2416$	$4$	2416.a	1.a	$1$	$8$	$8$	$142.549$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				302.4.a.b	$1$	$0$	$0$	$15$	$-22$	$77$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{2})q^{3}+(-3+\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
2416.4.a.d	$2416$	$4$	2416.a	1.a	$1$	$11$	$11$	$142.549$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓				302.4.a.d	$1$	$1$	$0$	$-15$	$28$	$-49$	$-$	$3$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(3-\beta _{5})q^{5}+(-4+\cdots)q^{7}+\cdots$
2416.4.a.e	$2416$	$4$	2416.a	1.a	$1$	$11$	$11$	$142.549$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓				302.4.a.c	$1$	$0$	$0$	$-9$	$-8$	$-45$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{6})q^{5}+(-4+\cdots)q^{7}+\cdots$
2416.4.a.f	$2416$	$4$	2416.a	1.a	$1$	$15$	$15$	$142.549$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓				151.4.a.a	$1$	$1$	$0$	$10$	$-61$	$26$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{6})q^{3}+(-4+\beta _{10})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
2416.4.a.g	$2416$	$4$	2416.a	1.a	$1$	$19$	$19$	$142.549$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓		✓		604.4.a.b	$1$	$1$	$0$	$-6$	$30$	$-30$	$-$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(2-\beta _{3})q^{5}+(-2-\beta _{14}+\cdots)q^{7}+\cdots$
2416.4.a.h	$2416$	$4$	2416.a	1.a	$1$	$19$	$19$	$142.549$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓				604.4.a.a	$1$	$0$	$0$	$12$	$-30$	$26$	$+$	$2^{9}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-2+\beta _{9})q^{5}+(1-\beta _{11}+\cdots)q^{7}+\cdots$
2416.4.a.i	$2416$	$4$	2416.a	1.a	$1$	$22$	$22$	$142.549$		$_{}$	None	None	✓		✓		151.4.a.b	$1$	$0$	$0$	$-8$	$59$	$-30$	$+$		$\mathrm{SU}(2)$
2416.4.a.j	$2416$	$4$	2416.a	1.a	$1$	$25$	$25$	$142.549$		$_{}$	None	None	✓				1208.4.a.b	$1$	$0$	$0$	$4$	$22$	$51$	$+$		$\mathrm{SU}(2)$
2416.4.a.k	$2416$	$4$	2416.a	1.a	$1$	$27$	$27$	$142.549$		$_{}$	None	None	✓				1208.4.a.c	$1$	$1$	$0$	$9$	$-52$	$25$	$-$		$\mathrm{SU}(2)$
2416.4.a.l	$2416$	$4$	2416.a	1.a	$1$	$29$	$29$	$142.549$		$_{}$	None	None	✓		✓		1208.4.a.d	$1$	$1$	$0$	$-19$	$-36$	$-53$	$-$		$\mathrm{SU}(2)$
2416.4.a.m	$2416$	$4$	2416.a	1.a	$1$	$30$	$30$	$142.549$		$_{}$	None	None	✓		✓		1208.4.a.e	$1$	$0$	$0$	$-3$	$58$	$-45$	$+$		$\mathrm{SU}(2)$

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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.