Cremona's table of elliptic curves

25215 = 3 · 5 · 41²

Field	Data	Notes
Atkin-Lehner	3- 5- 41+	Signs for the Atkin-Lehner involutions
Class	25215g	Isogeny class
Conductor	25215	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	1679360	Modular degree for the optimal curve
Δ	1.3424705447242E+21	Discriminant
Eigenvalues	1 3- 5- -4  0  4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8846298,-9973354697]	[a1,a2,a3,a4,a6]
Generators	[-1621:11190:1]	Generators of the group modulo torsion
j	233858751281/4100625	j-invariant
L	7.0378505754289	L(r)(E,1)/r!
Ω	0.087633718149146	Real period
R	5.0193654937211	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	75645k1 126075g1 25215c1	Quadratic twists by: -3 5 41

Hecke Eigenvalues for elliptic curve 25215g1

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	0	4	-4	0	0	8	-8	-6	+	12	-4	12	4	-14	-12	8	10	-8	4	8	-12

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Quadratic twists for elliptic curve 25215g1

-3	5	41
75645k1	126075g1	25215c1

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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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