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	1314f	Isogeny class
Conductor	1314	Conductor
∏ cp	216	Product of Tamagawa factors cp
Δ	6021726819581952 = 218 · 310 · 733	Discriminant
Eigenvalues	2- 3-  0 -4  6 -4  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-86765,9122645]	[a1,a2,a3,a4,a6]
j	99088945018143625/8260256268288	j-invariant
L	2.4906391143314	L(r)(E,1)/r!
Ω	0.41510651905524	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	10512t3 42048v3 438d3 32850r3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1314f3

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	-4	6	-4	6	8	0	0	8	2	6	2	0	12	-6	-10	-4	0	-	-16	-6	-6	14

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Quadratic twists for elliptic curve 1314f3

-4	8	-3	5	-7	73
10512t3	42048v3	438d3	32850r3	64386br3	95922g3

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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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