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	25200dc	Isogeny class
Conductor	25200	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	-693633024000000000 = -1 · 228 · 33 · 59 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7+  0  4  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-505875,-144168750]	[a1,a2,a3,a4,a6]
Generators	[27759:4623402:1]	Generators of the group modulo torsion
j	-66282611823/3211264	j-invariant
L	5.7342456669668	L(r)(E,1)/r!
Ω	0.089255160351666	Real period
R	8.0306920691949	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	3150i1 100800kf1 25200dd1 25200dl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200dc1

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

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Quadratic twists for elliptic curve 25200dc1

-4	8	-3	5
3150i1	100800kf1	25200dd1	25200dl1

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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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