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	25200cy	Isogeny class
Conductor	25200	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	538207031250000 = 24 · 39 · 512 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-29700,1623375]	[a1,a2,a3,a4,a6]
Generators	[69195:672300:343]	Generators of the group modulo torsion
j	588791808/109375	j-invariant
L	5.9909912602421	L(r)(E,1)/r!
Ω	0.49435674326385	Real period
R	6.0593805403445	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	6300a3 100800jr3 25200cz1 5040v3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200cy3

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

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Quadratic twists for elliptic curve 25200cy3

-4	8	-3	5
6300a3	100800jr3	25200cz1	5040v3

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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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