Cremona's table of elliptic curves

2415 = 3 · 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	3- 5- 7+ 23+	Signs for the Atkin-Lehner involutions
Class	2415g	Isogeny class
Conductor	2415	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	1109390625 = 32 · 56 · 73 · 23	Discriminant
Eigenvalues	1 3- 5- 7+ -2  0 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1438,-21037]	[a1,a2,a3,a4,a6]
Generators	[79:560:1]	Generators of the group modulo torsion
j	328523283207001/1109390625	j-invariant
L	4.4657528262837	L(r)(E,1)/r!
Ω	0.77550428297593	Real period
R	1.9195049055249	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	38640cd1 7245j1 12075j1 16905b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2415g1

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	0	-2	-4	+	2	-2	-4	-10	-8	0	-12	6	-6	-4	-4	4	-2	12	-10	14

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Quadratic twists for elliptic curve 2415g1

-4	-3	5	-7	-23
38640cd1	7245j1	12075j1	16905b1	55545l1

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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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