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	1014b	Isogeny class
Conductor	1014	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	4992	Modular degree for the optimal curve
Δ	-152234930075904 = -1 · 28 · 36 · 138	Discriminant
Eigenvalues	2+ 3-  3  2  6 13+ -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-10482,722308]	[a1,a2,a3,a4,a6]
j	-156116857/186624	j-invariant
L	2.0918757339855	L(r)(E,1)/r!
Ω	0.52296893349637	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	8112u1 32448k1 3042m1 25350ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1014b1

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
+	-	3	2	6	+	-3	2	-6	3	-4	-7	-3	-10	6	3	0	-7	-10	6	-13	-4	-6	18	14

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Quadratic twists for elliptic curve 1014b1

-4	8	-3	5	-7	-11	13
8112u1	32448k1	3042m1	25350ca1	49686q1	122694de1	1014f1

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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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