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	8190bp	Isogeny class
Conductor	8190	Conductor
∏ cp	1920	Product of Tamagawa factors cp
deg	921600	Modular degree for the optimal curve
Δ	1.2947580802956E+22	Discriminant
Eigenvalues	2- 3- 5- 7+ -4 13-  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-6480392,-3215030709]	[a1,a2,a3,a4,a6]
Generators	[-1629:55739:1]	Generators of the group modulo torsion
j	41285728533151645510969/17760741842188800000	j-invariant
L	6.4142961735143	L(r)(E,1)/r!
Ω	0.098382352148794	Real period
R	0.54331358160432	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	65520en1 2730c1 40950bn1 57330ec1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8190bp1

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	-	6	-8	-8	-2	8	2	2	-8	12	-10	-4	2	-8	-4	-6	-8	-4	-14	-14

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Quadratic twists for elliptic curve 8190bp1

-4	-3	5	-7	13
65520en1	2730c1	40950bn1	57330ec1	106470br1

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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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