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	8034k	Isogeny class
Conductor	8034	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	1028352 = 28 · 3 · 13 · 103	Discriminant
Eigenvalues	2- 3- -2 -4  4 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-89,-327]	[a1,a2,a3,a4,a6]
j	78018694417/1028352	j-invariant
L	3.1110214149727	L(r)(E,1)/r!
Ω	1.5555107074864	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	64272t1 24102n1 104442m1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 8034k1

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
-	-	-2	-4	4	-	2	8	-4	6	-8	-6	-6	4	-8	2	4	14	-4	0	-2	16	4	10	18

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Quadratic twists for elliptic curve 8034k1

-4	-3	13
64272t1	24102n1	104442m1

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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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