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	25200eg	Isogeny class
Conductor	25200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	442368	Modular degree for the optimal curve
Δ	282175488000000000 = 220 · 39 · 59 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 -2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1791075,922257250]	[a1,a2,a3,a4,a6]
j	13619385906841/6048000	j-invariant
L	1.2152523979172	L(r)(E,1)/r!
Ω	0.30381309947925	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3150k1 100800mw1 8400cf1 5040bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200eg1

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	-2	-6	-8	0	-6	4	10	6	-4	0	-6	-12	-10	-4	12	10	-8	-12	6	10

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Quadratic twists for elliptic curve 25200eg1

-4	8	-3	5
3150k1	100800mw1	8400cf1	5040bc1

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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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