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	25200fr	Isogeny class
Conductor	25200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48000	Modular degree for the optimal curve
Δ	-40824000000000 = -1 · 212 · 36 · 59 · 7	Discriminant
Eigenvalues	2- 3- 5- 7- -3  1 -7  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,6000,-250000]	[a1,a2,a3,a4,a6]
Generators	[215875:2973125:1331]	Generators of the group modulo torsion
j	4096/7	j-invariant
L	5.241295186221	L(r)(E,1)/r!
Ω	0.33882414475731	Real period
R	7.7345361411229	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	1575i1 100800ps1 2800be1 25200fd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200fr1

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	-7	0	6	5	-2	2	-2	4	-3	-6	10	-8	-2	-8	6	5	-4	0	7

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Quadratic twists for elliptic curve 25200fr1

-4	8	-3	5
1575i1	100800ps1	2800be1	25200fd1

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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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