Cremona's table of elliptic curves

8034 = 2 · 3 · 13 · 103

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 103+	Signs for the Atkin-Lehner involutions
Class	8034g	Isogeny class
Conductor	8034	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	3200	Modular degree for the optimal curve
Δ	281125728 = 25 · 38 · 13 · 103	Discriminant
Eigenvalues	2- 3-  0 -1  3 13+ -7  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-248,1248]	[a1,a2,a3,a4,a6]
Generators	[4:16:1]	Generators of the group modulo torsion
j	1687284042625/281125728	j-invariant
L	7.3354473200478	L(r)(E,1)/r!
Ω	1.6575530155415	Real period
R	0.11063669233004	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	64272m1 24102f1 104442j1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 8034g1

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
-	-	0	-1	3	+	-7	0	-6	-8	0	8	-4	-8	-4	-1	-6	2	-1	10	9	-10	2	-6	8

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Quadratic twists for elliptic curve 8034g1

-4	-3	13
64272m1	24102f1	104442j1

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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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