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	25200ds	Isogeny class
Conductor	25200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	-2285621452800 = -1 · 213 · 313 · 52 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+  2 -1 -1 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4395,-133670]	[a1,a2,a3,a4,a6]
Generators	[311:5346:1]	Generators of the group modulo torsion
j	-125768785/30618	j-invariant
L	4.9677760011562	L(r)(E,1)/r!
Ω	0.28945780310354	Real period
R	2.1452936956148	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3150bj1 100800lk1 8400ca1 25200fm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200ds1

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	-1	-1	-4	-7	-1	-3	6	3	-1	12	11	-3	5	-12	4	14	2	3	-10	10

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Quadratic twists for elliptic curve 25200ds1

-4	8	-3	5
3150bj1	100800lk1	8400ca1	25200fm1

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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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