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	25200fq	Isogeny class
Conductor	25200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-163296000 = -1 · 28 · 36 · 53 · 7	Discriminant
Eigenvalues	2- 3- 5- 7-  3 -1 -5  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-360,2700]	[a1,a2,a3,a4,a6]
Generators	[10:-10:1]	Generators of the group modulo torsion
j	-221184/7	j-invariant
L	5.8918099848631	L(r)(E,1)/r!
Ω	1.8079940434075	Real period
R	0.81468879921733	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	6300v1 100800pu1 2800bf1 25200fa1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200fq1

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
-	-	-	-	3	-1	-5	8	-2	1	2	-10	6	-4	-11	6	-10	0	-10	0	10	7	-12	-8	-3

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Quadratic twists for elliptic curve 25200fq1

-4	8	-3	5
6300v1	100800pu1	2800bf1	25200fa1

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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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