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	25200ee	Isogeny class
Conductor	25200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-2041200 = -1 · 24 · 36 · 52 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+ -5 -6 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-45,135]	[a1,a2,a3,a4,a6]
Generators	[6:9:1]	Generators of the group modulo torsion
j	-34560/7	j-invariant
L	4.2141397282397	L(r)(E,1)/r!
Ω	2.5070661033227	Real period
R	0.84045245609094	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	6300r1 100800mm1 2800p1 25200fu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200ee1

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
-	-	+	+	-5	-6	-4	6	3	3	-2	7	4	7	-2	10	-14	4	-3	-13	16	-1	10	-10	-2

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Quadratic twists for elliptic curve 25200ee1

-4	8	-3	5
6300r1	100800mm1	2800p1	25200fu1

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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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