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	31200a	Isogeny class
Conductor	31200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	117000000 = 26 · 32 · 56 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ -2  0 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-458,-3588]	[a1,a2,a3,a4,a6]
Generators	[-12:6:1]	Generators of the group modulo torsion
j	10648000/117	j-invariant
L	3.7145470068724	L(r)(E,1)/r!
Ω	1.0325058655012	Real period
R	1.7988018911008	Regulator
r	1	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31200o1 62400hf2 93600dk1 1248j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200a1

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	0	+	-2	-2	-8	6	2	6	0	-4	-8	6	4	2	-2	4	2	12	12	12	18

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Quadratic twists for elliptic curve 31200a1

-4	8	-3	5
31200o1	62400hf2	93600dk1	1248j1

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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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