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	2415a	Isogeny class
Conductor	2415	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	472410225 = 36 · 52 · 72 · 232	Discriminant
Eigenvalues	-1 3+ 5+ 7+  4 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-326,1874]	[a1,a2,a3,a4,a6]
Generators	[-16:65:1]	Generators of the group modulo torsion
j	3832302404449/472410225	j-invariant
L	1.5362122245112	L(r)(E,1)/r!
Ω	1.604558314567	Real period
R	0.9574050444691	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	38640ct2 7245p2 12075s2 16905z2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2415a2

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

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Quadratic twists for elliptic curve 2415a2

-4	-3	5	-7	-23
38640ct2	7245p2	12075s2	16905z2	55545f2

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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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