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	5070r	Isogeny class
Conductor	5070	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	34944	Modular degree for the optimal curve
Δ	-3425285926707840 = -1 · 27 · 38 · 5 · 138	Discriminant
Eigenvalues	2- 3+ 5- -3  1 13+  0 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-22565,3093995]	[a1,a2,a3,a4,a6]
Generators	[915:26920:1]	Generators of the group modulo torsion
j	-1557701041/4199040	j-invariant
L	4.7687439716015	L(r)(E,1)/r!
Ω	0.39325965803935	Real period
R	0.28871896929232	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	40560cv1 15210k1 25350bd1 5070b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070r1

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
-	+	-	-3	1	+	0	-5	-4	0	10	-1	6	-2	-9	-13	4	-2	-12	-2	-16	-10	12	1	12

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Quadratic twists for elliptic curve 5070r1

-4	-3	5	13
40560cv1	15210k1	25350bd1	5070b1

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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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