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	5070t	Isogeny class
Conductor	5070	Conductor
∏ cp	720	Product of Tamagawa factors cp
deg	120960	Modular degree for the optimal curve
Δ	-1.9761264961776E+19	Discriminant
Eigenvalues	2- 3- 5+ -2  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,675574,8108580]	[a1,a2,a3,a4,a6]
Generators	[196:12070:1]	Generators of the group modulo torsion
j	7064514799444439/4094064000000	j-invariant
L	5.9665387560509	L(r)(E,1)/r!
Ω	0.12997156027387	Real period
R	0.25503608223037	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	40560bi1 15210u1 25350c1 390d1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070t1

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	0	+	0	-2	-6	0	-8	-2	-6	-4	0	-6	0	14	4	0	4	-16	12	6	4

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Quadratic twists for elliptic curve 5070t1

-4	-3	5	13
40560bi1	15210u1	25350c1	390d1

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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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