Cremona's table of elliptic curves

1314 = 2 · 3² · 73

Field	Data	Notes
Atkin-Lehner	2+ 3- 73-	Signs for the Atkin-Lehner involutions
Class	1314c	Isogeny class
Conductor	1314	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-745283436804 = -1 · 22 · 38 · 734	Discriminant
Eigenvalues	2+ 3-  2 -4  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,729,40657]	[a1,a2,a3,a4,a6]
Generators	[-9:187:1]	Generators of the group modulo torsion
j	58727785103/1022336676	j-invariant
L	2.0699063212824	L(r)(E,1)/r!
Ω	0.67033831262643	Real period
R	0.77196330654753	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	10512v4 42048bb3 438f4 32850bo3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1314c4

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

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Quadratic twists for elliptic curve 1314c4

-4	8	-3	5	-7	73
10512v4	42048bb3	438f4	32850bo3	64386s3	95922e3

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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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