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	25215b	Isogeny class
Conductor	25215	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	743904	Modular degree for the optimal curve
Δ	9.8229552052993E+19	Discriminant
Eigenvalues	-1 3+ 5+  2  3 -1  8  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1161606,68959728]	[a1,a2,a3,a4,a6]
j	21708480289/12301875	j-invariant
L	1.3042391566091	L(r)(E,1)/r!
Ω	0.16302989457614	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75645r1 126075y1 25215f1	Quadratic twists by: -3 5 41

Hecke Eigenvalues for elliptic curve 25215b1

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	+	+	2	3	-1	8	6	-1	-2	0	-3	-	-4	-8	10	-9	5	10	-5	9	10	-9	16	10

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Quadratic twists for elliptic curve 25215b1

-3	5	41
75645r1	126075y1	25215f1

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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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