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
deg	3120	Modular degree for the optimal curve
Δ	-41230293562224 = -1 · 24 · 35 · 139	Discriminant
Eigenvalues	2- 3-  2  2  0 13-  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,8193,-117495]	[a1,a2,a3,a4,a6]
j	5735339/3888	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	8112w1 32448r1 3042g1 25350k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1014g1

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 1014g1

-4	8	-3	5	-7	-11	13
8112w1	32448r1	3042g1	25350k1	49686cq1	122694bp1	1014c1

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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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