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	5070h	Isogeny class
Conductor	5070	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	336960	Modular degree for the optimal curve
Δ	2.533189236463E+20	Discriminant
Eigenvalues	2+ 3+ 5-  0  6 13-  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3795912,-2743222464]	[a1,a2,a3,a4,a6]
Generators	[-1233:8649:1]	Generators of the group modulo torsion
j	570403428460237/23887872000	j-invariant
L	2.790642644016	L(r)(E,1)/r!
Ω	0.10844059993275	Real period
R	4.2890495591542	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	40560da1 15210bl1 25350dc1 5070p1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070h1

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	6	-	6	-6	-6	-6	0	-6	-12	-8	0	-12	6	10	0	12	-6	-8	0	0	6

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Quadratic twists for elliptic curve 5070h1

-4	-3	5	13
40560da1	15210bl1	25350dc1	5070p1

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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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