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	25200cg	Isogeny class
Conductor	25200	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	76800	Modular degree for the optimal curve
Δ	-1883294043750000 = -1 · 24 · 316 · 58 · 7	Discriminant
Eigenvalues	2+ 3- 5- 7- -1  4 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-15375,2213125]	[a1,a2,a3,a4,a6]
j	-88218880/413343	j-invariant
L	2.4418258662448	L(r)(E,1)/r!
Ω	0.4069709777075	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12600y1 100800pi1 8400bf1 25200y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200cg1

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
+	-	-	-	-1	4	-2	4	-3	1	6	-3	0	-5	4	-6	-4	-4	5	-1	10	1	14	8	-14

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Quadratic twists for elliptic curve 25200cg1

-4	8	-3	5
12600y1	100800pi1	8400bf1	25200y1

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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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