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	2415f	Isogeny class
Conductor	2415	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	734582625 = 3 · 53 · 7 · 234	Discriminant
Eigenvalues	-1 3- 5+ 7-  4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-231,336]	[a1,a2,a3,a4,a6]
j	1363569097969/734582625	j-invariant
L	1.3996460788421	L(r)(E,1)/r!
Ω	1.3996460788421	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38640bg1 7245s1 12075c1 16905q1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2415f1

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	-2	0	-	6	-8	10	-2	4	-8	6	-4	10	-12	-12	-10	16	0	6	-2

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Quadratic twists for elliptic curve 2415f1

-4	-3	5	-7	-23
38640bg1	7245s1	12075c1	16905q1	55545u1

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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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