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	8190bf	Isogeny class
Conductor	8190	Conductor
∏ cp	432	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	801335808000 = 212 · 33 · 53 · 73 · 132	Discriminant
Eigenvalues	2- 3+ 5- 7- -6 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3512,68411]	[a1,a2,a3,a4,a6]
Generators	[-59:289:1]	Generators of the group modulo torsion
j	177381177331203/29679104000	j-invariant
L	6.6444509259149	L(r)(E,1)/r!
Ω	0.85405527789689	Real period
R	0.64832366025503	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	65520cg1 8190b3 40950d1 57330dc1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8190bf1

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
-	+	-	-	-6	-	0	-4	0	0	-4	-4	6	-10	-6	6	0	-10	-4	6	2	-4	-6	6	-10

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Quadratic twists for elliptic curve 8190bf1

-4	-3	5	-7	13
65520cg1	8190b3	40950d1	57330dc1	106470e1

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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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