Cremona's table of elliptic curves

2475 = 3² · 5² · 11

Field	Data	Notes
Atkin-Lehner	3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	2475a	Isogeny class
Conductor	2475	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	51046875 = 33 · 56 · 112	Discriminant
Eigenvalues	1 3+ 5+  2 11+  2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-417,3366]	[a1,a2,a3,a4,a6]
Generators	[-6:78:1]	Generators of the group modulo torsion
j	19034163/121	j-invariant
L	3.9615524723551	L(r)(E,1)/r!
Ω	2.0117692895983	Real period
R	0.98459413135442	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	39600cf2 2475d2 99a2 121275s2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2475a2

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

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Quadratic twists for elliptic curve 2475a2

-4	-3	5	-7	-11
39600cf2	2475d2	99a2	121275s2	27225l2

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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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