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	25200dx	Isogeny class
Conductor	25200	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	185177664000000 = 212 · 310 · 56 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+  4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14475,-143750]	[a1,a2,a3,a4,a6]
Generators	[-91:648:1]	Generators of the group modulo torsion
j	7189057/3969	j-invariant
L	5.3226195213988	L(r)(E,1)/r!
Ω	0.4659099872766	Real period
R	1.4280171242173	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	1575g2 100800me2 8400cd2 1008k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200dx2

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	2	-6	-4	0	2	0	-6	-2	-4	0	6	12	-2	4	0	6	16	12	14	-18

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Quadratic twists for elliptic curve 25200dx2

-4	8	-3	5
1575g2	100800me2	8400cd2	1008k2

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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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