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	8190a	Isogeny class
Conductor	8190	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-1719900 = -1 · 22 · 33 · 52 · 72 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  4 13+ -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,30,0]	[a1,a2,a3,a4,a6]
Generators	[3:9:1]	Generators of the group modulo torsion
j	108531333/63700	j-invariant
L	2.8695116406612	L(r)(E,1)/r!
Ω	1.6102030491322	Real period
R	0.44552015384142	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	65520bx1 8190be1 40950df1 57330k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8190a1

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

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Quadratic twists for elliptic curve 8190a1

-4	-3	5	-7	13
65520bx1	8190be1	40950df1	57330k1	106470dv1

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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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