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	8190bt	Isogeny class
Conductor	8190	Conductor
∏ cp	240	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	60866297856000 = 220 · 36 · 53 · 72 · 13	Discriminant
Eigenvalues	2- 3- 5- 7- -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-18002,-845999]	[a1,a2,a3,a4,a6]
Generators	[-79:319:1]	Generators of the group modulo torsion
j	884984855328729/83492864000	j-invariant
L	6.6358644197243	L(r)(E,1)/r!
Ω	0.41465911361983	Real period
R	0.26671966609695	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	65520dl1 910a1 40950bg1 57330el1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8190bt1

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	-8	2	4	10	6	0	-8	-2	-12	-2	-4	-12	-2	-8	-4	-2	14

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Quadratic twists for elliptic curve 8190bt1

-4	-3	5	-7	13
65520dl1	910a1	40950bg1	57330el1	106470be1

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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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