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	5070i	Isogeny class
Conductor	5070	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-1338796875000 = -1 · 23 · 3 · 59 · 134	Discriminant
Eigenvalues	2+ 3- 5+  2 -3 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,1686,49012]	[a1,a2,a3,a4,a6]
j	18573478391/46875000	j-invariant
L	1.7973824456476	L(r)(E,1)/r!
Ω	0.59912748188253	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40560bj2 15210bp2 25350bz2 5070u2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070i2

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
+	-	+	2	-3	+	6	2	3	3	5	-7	6	-1	-3	-6	-9	2	8	-12	14	5	-6	-18	14

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Quadratic twists for elliptic curve 5070i2

-4	-3	5	13
40560bj2	15210bp2	25350bz2	5070u2

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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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