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	5070o	Isogeny class
Conductor	5070	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12480	Modular degree for the optimal curve
Δ	-3181349811900 = -1 · 22 · 3 · 52 · 139	Discriminant
Eigenvalues	2- 3+ 5+  0  4 13- -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-7186,246683]	[a1,a2,a3,a4,a6]
Generators	[61:169:1]	Generators of the group modulo torsion
j	-3869893/300	j-invariant
L	4.6760836850099	L(r)(E,1)/r!
Ω	0.78217852099401	Real period
R	2.9891409438522	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	40560cm1 15210w1 25350bj1 5070g1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070o1

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 5070o1

-4	-3	5	13
40560cm1	15210w1	25350bj1	5070g1

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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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