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	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	122611968 = 28 · 38 · 73	Discriminant
Eigenvalues	2+ 3-  2 -4  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-171,-635]	[a1,a2,a3,a4,a6]
Generators	[-7:17:1]	Generators of the group modulo torsion
j	761048497/168192	j-invariant
L	2.0699063212824	L(r)(E,1)/r!
Ω	1.3406766252529	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	10512v1 42048bb1 438f1 32850bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1314c1

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 1314c1

-4	8	-3	5	-7	73
10512v1	42048bb1	438f1	32850bo1	64386s1	95922e1

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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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