Cremona's table of elliptic curves

31200 = 2⁵ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	31200c	Isogeny class
Conductor	31200	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	589824	Modular degree for the optimal curve
Δ	2927948765625000000 = 26 · 38 · 512 · 134	Discriminant
Eigenvalues	2+ 3+ 5+  4  0 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-406758,56638512]	[a1,a2,a3,a4,a6]
Generators	[141947:12157894:2197]	Generators of the group modulo torsion
j	7442744143086784/2927948765625	j-invariant
L	5.3506180189377	L(r)(E,1)/r!
Ω	0.23096147344753	Real period
R	11.583356174235	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	31200p1 62400hk2 93600dn1 6240bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200c1

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
+	+	+	4	0	+	-2	-8	4	6	8	-6	-6	-4	4	-6	-8	-10	4	-8	14	0	12	-6	6

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Quadratic twists for elliptic curve 31200c1

-4	8	-3	5
31200p1	62400hk2	93600dn1	6240bf1

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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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