Cremona's table of elliptic curves

12402 = 2 · 3² · 13 · 53

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 53-	Signs for the Atkin-Lehner involutions
Class	12402g	Isogeny class
Conductor	12402	Conductor
∏ cp	156	Product of Tamagawa factors cp
deg	254592	Modular degree for the optimal curve
Δ	-685618068266606592 = -1 · 213 · 39 · 134 · 533	Discriminant
Eigenvalues	2- 3+  2  1  1 13+ -6 -3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1990604,-1081235249]	[a1,a2,a3,a4,a6]
Generators	[9853:962429:1]	Generators of the group modulo torsion
j	-44318681593817709051/34833006567424	j-invariant
L	8.0859605539368	L(r)(E,1)/r!
Ω	0.063548146442639	Real period
R	0.81565054805713	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	99216v1 12402a1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 12402g1

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
-	+	2	1	1	+	-6	-3	-7	-1	-2	-6	9	4	-8	-	-4	-5	7	1	-16	-10	-12	12	5

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Quadratic twists for elliptic curve 12402g1

-4	-3
99216v1	12402a1

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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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