Cremona's table of elliptic curves

4134 = 2 · 3 · 13 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 53-	Signs for the Atkin-Lehner involutions
Class	4134g	Isogeny class
Conductor	4134	Conductor
∏ cp	272	Product of Tamagawa factors cp
deg	8704	Modular degree for the optimal curve
Δ	-7702692102144 = -1 · 217 · 38 · 132 · 53	Discriminant
Eigenvalues	2- 3- -1 -2 -3 13-  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,4929,-9063]	[a1,a2,a3,a4,a6]
Generators	[102:-1299:1]	Generators of the group modulo torsion
j	13243252505373071/7702692102144	j-invariant
L	5.5812854014834	L(r)(E,1)/r!
Ω	0.43825589156891	Real period
R	0.046820663493292	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	33072q1 12402e1 103350a1 53742i1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4134g1

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	-3	-	3	-2	-5	-6	7	-8	-6	-11	12	-	3	-2	2	-16	-2	7	6	7	-7

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Quadratic twists for elliptic curve 4134g1

-4	-3	5	13
33072q1	12402e1	103350a1	53742i1

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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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