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	1014c	Isogeny class
Conductor	1014	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	20247552 = 210 · 32 · 133	Discriminant
Eigenvalues	2+ 3- -2 -2  0 13-  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-70997,7275296]	[a1,a2,a3,a4,a6]
Generators	[147:70:1]	Generators of the group modulo torsion
j	18013780041269221/9216	j-invariant
L	1.9424336989416	L(r)(E,1)/r!
Ω	1.3173935460676	Real period
R	0.7372260569895	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8112y4 32448p4 3042n4 25350cc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1014c4

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 1014c4

-4	8	-3	5	-7	-11	13
8112y4	32448p4	3042n4	25350cc4	49686w4	122694dk4	1014g4

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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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