Cremona's table of elliptic curves

8190 = 2 · 3² · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	8190k	Isogeny class
Conductor	8190	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3265122656250 = 2 · 38 · 58 · 72 · 13	Discriminant
Eigenvalues	2+ 3- 5+ 7+  4 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-550485,157342675]	[a1,a2,a3,a4,a6]
Generators	[431:-130:1]	Generators of the group modulo torsion
j	25306558948218234961/4478906250	j-invariant
L	3.0003379166953	L(r)(E,1)/r!
Ω	0.62639081722197	Real period
R	2.394940853381	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	65520dg6 2730w5 40950ef6 57330cg6	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8190k5

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

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Quadratic twists for elliptic curve 8190k5

-4	-3	5	-7	13
65520dg6	2730w5	40950ef6	57330cg6	106470gb6

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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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