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	31200x	Isogeny class
Conductor	31200	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	-3080025000000000000 = -1 · 212 · 36 · 514 · 132	Discriminant
Eigenvalues	2+ 3- 5+ -2  2 13-  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-173633,-88969137]	[a1,a2,a3,a4,a6]
Generators	[703:11700:1]	Generators of the group modulo torsion
j	-9045718037056/48125390625	j-invariant
L	6.9027819458157	L(r)(E,1)/r!
Ω	0.1052475616099	Real period
R	1.3663780424436	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31200bo2 62400l1 93600ei2 6240y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200x2

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
+	-	+	-2	2	-	2	2	8	-6	-2	-2	-2	0	-6	10	-14	-10	-2	-6	-2	-12	-6	-18	14

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Quadratic twists for elliptic curve 31200x2

-4	8	-3	5
31200bo2	62400l1	93600ei2	6240y2

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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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