Cremona's table of elliptic curves

91728 = 2⁴ · 3² · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	91728v	Isogeny class
Conductor	91728	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	294912	Modular degree for the optimal curve
Δ	-337663276763904 = -1 · 28 · 36 · 77 · 133	Discriminant
Eigenvalues	2+ 3- -1 7-  2 13+  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-29988,2185596]	[a1,a2,a3,a4,a6]
Generators	[105:441:1]	Generators of the group modulo torsion
j	-135834624/15379	j-invariant
L	5.4157197414923	L(r)(E,1)/r!
Ω	0.52583952470411	Real period
R	1.2873984091543	Regulator
r	1	Rank of the group of rational points
S	1.0000000001655	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	45864j1 10192d1 13104z1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 91728v1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	-1	-	2	+	0	-7	-3	9	5	-8	-10	-5	-7	-3	0	-6	10	4	11	11	-11	-3	15

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Quadratic twists for elliptic curve 91728v1

-4	-3	-7
45864j1	10192d1	13104z1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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