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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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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
725.1.g.a	$725$	$1$	725.g	29.c	$4$	$2$	$1$	$0.362$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{4}-iq^{9}+(-1-i)q^{11}-q^{16}+\cdots$
725.1.h.a	$725$	$1$	725.h	145.h	$4$	$2$	$1$	$0.362$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{29}) $		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{4}+(1-i)q^{7}+iq^{9}+(-1-i+\cdots)q^{13}+\cdots$
725.2.a.a	$725$	$2$	725.a	1.a	$1$	$1$	$1$	$5.789$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{7}-3q^{8}-3q^{9}-6q^{11}+\cdots$
725.2.a.b	$725$	$2$	725.a	1.a	$1$	$2$	$2$	$5.789$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots$
725.2.a.c	$725$	$2$	725.a	1.a	$1$	$2$	$2$	$5.789$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$4$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+(2+\cdots)q^{6}+\cdots$
725.2.a.d	$725$	$2$	725.a	1.a	$1$	$3$	$3$	$5.789$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$-3$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots$
725.2.a.e	$725$	$2$	725.a	1.a	$1$	$3$	$3$	$5.789$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
725.2.a.f	$725$	$2$	725.a	1.a	$1$	$4$	$4$	$5.789$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$
725.2.a.g	$725$	$2$	725.a	1.a	$1$	$4$	$4$	$5.789$	$\Q(\sqrt{3}, \sqrt{11})$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+q^{4}+(-2-\beta _{3})q^{6}+\cdots$
725.2.a.h	$725$	$2$	725.a	1.a	$1$	$5$	$5$	$5.789$	5.5.240881.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-6$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
725.2.a.i	$725$	$2$	725.a	1.a	$1$	$5$	$5$	$5.789$	5.5.294577.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$0$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
725.2.a.j	$725$	$2$	725.a	1.a	$1$	$5$	$5$	$5.789$	5.5.294577.1	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$0$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
725.2.a.k	$725$	$2$	725.a	1.a	$1$	$5$	$5$	$5.789$	5.5.240881.1	$_{}$	None	None	✓	$1$	$0$	$2$	$6$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
725.2.a.l	$725$	$2$	725.a	1.a	$1$	$6$	$6$	$5.789$	6.6.337383424.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots$
725.2.b.a	$725$	$2$	725.b	5.b	$2$	$2$	$2$	$5.789$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+2iq^{7}+3iq^{8}+3q^{9}+\cdots$
725.2.b.b	$725$	$2$	725.b	5.b	$2$	$4$	$4$	$5.789$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
725.2.b.c	$725$	$2$	725.b	5.b	$2$	$4$	$4$	$5.789$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots$
725.2.b.d	$725$	$2$	725.b	5.b	$2$	$6$	$6$	$5.789$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-2-\beta _{3}+\cdots)q^{4}+\cdots$
725.2.b.e	$725$	$2$	725.b	5.b	$2$	$6$	$6$	$5.789$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots$
725.2.b.f	$725$	$2$	725.b	5.b	$2$	$10$	$10$	$5.789$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
725.2.b.g	$725$	$2$	725.b	5.b	$2$	$10$	$10$	$5.789$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{2}+\beta _{7})q^{3}+(-1+\beta _{5}+\cdots)q^{4}+\cdots$
725.2.c.a	$725$	$2$	725.c	29.b	$2$	$2$	$2$	$5.789$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-3q^{4}-2q^{7}-\beta q^{8}+3q^{9}+\cdots$
725.2.c.b	$725$	$2$	725.c	29.b	$2$	$2$	$2$	$5.789$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-3q^{4}+2q^{7}-\beta q^{8}+3q^{9}+\cdots$
725.2.c.c	$725$	$2$	725.c	29.b	$2$	$2$	$2$	$5.789$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-\beta q^{3}-3q^{4}+5q^{6}-2q^{7}+\cdots$
725.2.c.d	$725$	$2$	725.c	29.b	$2$	$4$	$4$	$5.789$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots$
725.2.c.e	$725$	$2$	725.c	29.b	$2$	$6$	$6$	$5.789$	6.0.16516096.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
725.2.c.f	$725$	$2$	725.c	29.b	$2$	$8$	$8$	$5.789$	8.0.1731891456.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}-\beta _{5}q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
725.2.c.g	$725$	$2$	725.c	29.b	$2$	$10$	$10$	$5.789$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$
725.2.c.h	$725$	$2$	725.c	29.b	$2$	$10$	$10$	$5.789$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$
725.2.d.a	$725$	$2$	725.d	145.d	$2$	$4$	$4$	$5.789$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}+3q^{4}+5q^{6}-2\beta _{1}q^{7}+\cdots$
725.2.d.b	$725$	$2$	725.d	145.d	$2$	$8$	$8$	$5.789$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{24}^{6}q^{2}+(\zeta_{24}^{3}-\zeta_{24}^{6})q^{3}+\zeta_{24}^{2}q^{4}+\cdots$
725.2.d.c	$725$	$2$	725.d	145.d	$2$	$12$	$12$	$5.789$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(\beta _{5}-\beta _{7})q^{3}+(1+\beta _{4})q^{4}+\cdots$
725.2.d.d	$725$	$2$	725.d	145.d	$2$	$20$	$20$	$5.789$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{16}q^{3}+(1-\beta _{9})q^{4}+(1+\cdots)q^{6}+\cdots$
725.2.e.a	$725$	$2$	725.e	145.e	$4$	$4$	$2$	$5.789$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}-3q^{4}+(-\beta _{2}+\beta _{3})q^{7}-\beta _{2}q^{8}+\cdots$
725.2.e.b	$725$	$2$	725.e	145.e	$4$	$16$	$8$	$5.789$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{7}q^{2}+\beta _{9}q^{3}-\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots$
725.2.e.c	$725$	$2$	725.e	145.e	$4$	$26$	$13$	$5.789$		$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$4$			$\mathrm{SU}(2)[C_{4}]$
725.2.e.d	$725$	$2$	725.e	145.e	$4$	$40$	$20$	$5.789$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
725.2.j.a	$725$	$2$	725.j	145.j	$4$	$4$	$2$	$5.789$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+3q^{4}+(\beta _{2}-\beta _{3})q^{7}+\beta _{3}q^{8}+\cdots$
725.2.j.b	$725$	$2$	725.j	145.j	$4$	$16$	$8$	$5.789$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots$
725.2.j.c	$725$	$2$	725.j	145.j	$4$	$26$	$13$	$5.789$		$_{}$	None	None		$2$	$0$	$6$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{4}]$
725.2.j.d	$725$	$2$	725.j	145.j	$4$	$40$	$20$	$5.789$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
725.2.k.a	$725$	$2$	725.k	25.d	$5$	$4$	$1$	$5.789$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-5$	$-12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+2\zeta_{10}^{3}q^{4}+\cdots$
725.2.k.b	$725$	$2$	725.k	25.d	$5$	$128$	$32$	$5.789$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$3$	$-2$			$\mathrm{SU}(2)[C_{5}]$
725.2.k.c	$725$	$2$	725.k	25.d	$5$	$148$	$37$	$5.789$		$_{}$	None	None		$2$	$0$	$0$	$2$	$8$	$10$			$\mathrm{SU}(2)[C_{5}]$
725.2.l.a	$725$	$2$	725.l	29.d	$7$	$6$	$1$	$5.789$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$-3$	$-7$	$0$	$7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(-1+\cdots)q^{3}+\cdots$
725.2.l.b	$725$	$2$	725.l	29.d	$7$	$6$	$1$	$5.789$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$2$	$5$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots$
725.2.l.c	$725$	$2$	725.l	29.d	$7$	$6$	$1$	$5.789$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$3$	$7$	$0$	$-7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+(1-\zeta_{14}^{2}+\cdots)q^{3}+\cdots$
725.2.l.d	$725$	$2$	725.l	29.d	$7$	$24$	$4$	$5.789$		$_{}$	None	None		$2$	$0$	$2$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{7}]$
725.2.l.e	$725$	$2$	725.l	29.d	$7$	$36$	$6$	$5.789$		$_{}$	None	None		$2$	$0$	$2$	$2$	$0$	$8$			$\mathrm{SU}(2)[C_{7}]$
725.2.l.f	$725$	$2$	725.l	29.d	$7$	$54$	$9$	$5.789$		$_{}$	None	None		$2$	$0$	$-1$	$-7$	$0$	$3$			$\mathrm{SU}(2)[C_{7}]$

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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.