Cremona's table of elliptic curves

1014 = 2 · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13-	Signs for the Atkin-Lehner involutions
Class	1014g	Isogeny class
Conductor	1014	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	-33358870603628544 = -1 · 220 · 3 · 139	Discriminant
Eigenvalues	2- 3-  2  2  0 13-  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-749772,249978000]	[a1,a2,a3,a4,a6]
j	-4395631034341/3145728	j-invariant
L	3.6537922925477	L(r)(E,1)/r!
Ω	0.36537922925477	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	8112w3 32448r3 3042g3 25350k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1014g3

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

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Quadratic twists for elliptic curve 1014g3

-4	8	-3	5	-7	-11	13
8112w3	32448r3	3042g3	25350k3	49686cq3	122694bp3	1014c3

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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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