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	5070k	Isogeny class
Conductor	5070	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	52420691525582250 = 2 · 32 · 53 · 1312	Discriminant
Eigenvalues	2+ 3- 5- -2  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-202128,-33214244]	[a1,a2,a3,a4,a6]
Generators	[-298:909:1]	Generators of the group modulo torsion
j	189208196468929/10860320250	j-invariant
L	3.4140355069207	L(r)(E,1)/r!
Ω	0.22596771246534	Real period
R	2.5180850468068	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	40560br4 15210bf4 25350bx4 390c4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070k4

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	4	-2	6	-4	0	-6	0	-10	-8	0	-8	8	12	-6	-8

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Quadratic twists for elliptic curve 5070k4

-4	-3	5	13
40560br4	15210bf4	25350bx4	390c4

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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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