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	4	Product of Tamagawa factors cp
Δ	197730 = 2 · 32 · 5 · 133	Discriminant
Eigenvalues	2+ 3+ 5-  0 -4 13- -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-692,6726]	[a1,a2,a3,a4,a6]
Generators	[5:56:1]	Generators of the group modulo torsion
j	16718302693/90	j-invariant
L	2.4325503673099	L(r)(E,1)/r!
Ω	2.8201847640105	Real period
R	0.86254999968537	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	40560cz2 15210bk2 25350db2 5070o2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070g2

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 5070g2

-4	-3	5	13
40560cz2	15210bk2	25350db2	5070o2

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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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