Cremona's table of elliptic curves

5046 = 2 · 3 · 29²

Field	Data	Notes
Atkin-Lehner	2+ 3- 29-	Signs for the Atkin-Lehner involutions
Class	5046g	Isogeny class
Conductor	5046	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	76560	Modular degree for the optimal curve
Δ	9220541883697152 = 211 · 32 · 298	Discriminant
Eigenvalues	2+ 3- -4 -3  2 -6  7  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-75708,6546682]	[a1,a2,a3,a4,a6]
Generators	[70:1226:1]	Generators of the group modulo torsion
j	95930521/18432	j-invariant
L	2.2821245090556	L(r)(E,1)/r!
Ω	0.38958035184331	Real period
R	0.97631742217733	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	40368be1 15138be1 126150ci1 5046j1	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 5046g1

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
+	-	-4	-3	2	-6	7	4	-3	-	-1	6	-6	6	7	-6	-10	10	14	-5	-1	-11	-6	-7	-3

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Quadratic twists for elliptic curve 5046g1

-4	-3	5	29
40368be1	15138be1	126150ci1	5046j1

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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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