Cremona's table of elliptic curves

25200 = 2⁴ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	25200eb	Isogeny class
Conductor	25200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	98304	Modular degree for the optimal curve
Δ	-752467968000000 = -1 · 220 · 38 · 56 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14475,1480250]	[a1,a2,a3,a4,a6]
Generators	[70:900:1]	Generators of the group modulo torsion
j	-7189057/16128	j-invariant
L	4.3133276759677	L(r)(E,1)/r!
Ω	0.44867833745014	Real period
R	2.4033518647683	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	3150bl1 100800lz1 8400bl1 1008l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200eb1

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

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Quadratic twists for elliptic curve 25200eb1

-4	8	-3	5
3150bl1	100800lz1	8400bl1	1008l1

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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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