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	9	Product of Tamagawa factors cp
deg	3024	Modular degree for the optimal curve
Δ	-192786750 = -1 · 2 · 33 · 53 · 134	Discriminant
Eigenvalues	2+ 3- 5+  2 -3 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-849,9466]	[a1,a2,a3,a4,a6]
j	-2365581049/6750	j-invariant
L	1.7973824456476	L(r)(E,1)/r!
Ω	1.7973824456476	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	40560bj1 15210bp1 25350bz1 5070u1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070i1

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 5070i1

-4	-3	5	13
40560bj1	15210bp1	25350bz1	5070u1

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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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