Cremona's table of elliptic curves

5070 = 2 · 3 · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 13-	Signs for the Atkin-Lehner involutions
Class	5070g	Isogeny class
Conductor	5070	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-659100 = -1 · 22 · 3 · 52 · 133	Discriminant
Eigenvalues	2+ 3+ 5-  0 -4 13- -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-42,96]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	-3869893/300	j-invariant
L	2.4325503673099	L(r)(E,1)/r!
Ω	2.8201847640105	Real period
R	0.43127499984268	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	40560cz1 15210bk1 25350db1 5070o1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070g1

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
+	+	-	0	-4	-	-4	4	-6	4	10	4	-2	12	0	-2	-4	-10	-10	12	-6	-8	0	10	-14

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Quadratic twists for elliptic curve 5070g1

-4	-3	5	13
40560cz1	15210bk1	25350db1	5070o1

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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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