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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 (25 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
3375.1.c.a	$3375$	$1$	3375.c	3.b	$2$	$8$	$8$	$1.684$	8.0.324000000.1	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}+(-2-\beta _{2}+\beta _{6}+\cdots)q^{4}+\cdots$
3375.1.d.a	$3375$	$1$	3375.d	15.d	$2$	$4$	$4$	$1.684$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{8}+\cdots$
3375.1.d.b	$3375$	$1$	3375.d	15.d	$2$	$4$	$4$	$1.684$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{8}+\cdots$
3375.1.g.a	$3375$	$1$	3375.g	5.c	$4$	$16$	$8$	$1.684$	16.0.$\cdots$.2	$D_{30}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{14}q^{2}+(-\beta _{4}-\beta _{7})q^{4}+(\beta _{6}-\beta _{9}+\cdots)q^{8}+\cdots$
3375.1.m.a	$3375$	$1$	3375.m	75.h	$10$	$8$	$2$	$1.684$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$-6$	$0$	$0$	$0$		$1$		$q+(-1+\zeta_{20}^{2})q^{2}+(1-\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{4}+\cdots$
3375.1.m.b	$3375$	$1$	3375.m	75.h	$10$	$8$	$2$	$1.684$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$6$	$0$	$0$	$0$		$1$		$q+(1-\zeta_{20}^{2})q^{2}+(1-\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{4}+\cdots$
3375.1.o.a	$3375$	$1$	3375.o	75.j	$10$	$8$	$2$	$1.684$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{2}+(-1-\zeta_{20}^{4}+\cdots)q^{4}+\cdots$
3375.2.a.a	$3375$	$2$	3375.a	1.a	$1$	$4$	$4$	$26.950$	$\Q(\zeta_{15})^+$	$_{}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-4$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(5-\beta _{1}+\cdots)q^{4}+\cdots$
3375.2.a.b	$3375$	$2$	3375.a	1.a	$1$	$4$	$4$	$26.950$	$\Q(\zeta_{15})^+$	$_{}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{4}+(1-\beta _{2})q^{8}+\cdots$
3375.2.a.c	$3375$	$2$	3375.a	1.a	$1$	$4$	$4$	$26.950$	$\Q(\zeta_{15})^+$	$_{}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{1}q^{4}+(-1+\beta _{2}+\cdots)q^{8}+\cdots$
3375.2.a.d	$3375$	$2$	3375.a	1.a	$1$	$4$	$4$	$26.950$	$\Q(\zeta_{15})^+$	$_{}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1+\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$
3375.2.a.e	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$-6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}-\beta _{6})q^{2}+(-1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
3375.2.a.f	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
3375.2.a.g	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
3375.2.a.h	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{2}+\beta _{4})q^{4}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
3375.2.a.i	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{2}+\beta _{4})q^{4}+(1+\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$
3375.2.a.j	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$0$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2}+\beta _{7})q^{7}+\cdots$
3375.2.a.k	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2}-\beta _{7})q^{7}+\cdots$
3375.2.a.l	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{2}+\beta _{4})q^{4}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
3375.2.a.m	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{2}+\beta _{4})q^{4}+(1+\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$
3375.2.a.n	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$0$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2}+\beta _{7})q^{7}+\cdots$
3375.2.a.o	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2}-\beta _{7})q^{7}+\cdots$
3375.2.a.p	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{7}+\cdots$
3375.2.a.q	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{7}+\cdots$
3375.2.a.r	$3375$	$2$	3375.a	1.a	$1$	$8$	$8$	$26.950$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{2}+\beta _{6})q^{2}+(-1-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$

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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.