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	1314a	Isogeny class
Conductor	1314	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	163349794368 = 26 · 38 · 733	Discriminant
Eigenvalues	2+ 3-  0  2  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-656442,204875892]	[a1,a2,a3,a4,a6]
Generators	[1644:58902:1]	Generators of the group modulo torsion
j	42912679782639390625/224073792	j-invariant
L	2.0895657322661	L(r)(E,1)/r!
Ω	0.69347345131445	Real period
R	4.5197816765129	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	10512s3 42048q3 438a3 32850bm3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1314a3

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
+	-	0	2	0	-4	-6	-4	0	0	2	2	-6	-4	6	12	0	-10	-4	-12	-	-4	0	-6	2

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Quadratic twists for elliptic curve 1314a3

-4	8	-3	5	-7	73
10512s3	42048q3	438a3	32850bm3	64386o3	95922d3

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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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