Cremona's table of elliptic curves

2714 = 2 · 23 · 59

Field	Data	Notes
Atkin-Lehner	2+ 23- 59-	Signs for the Atkin-Lehner involutions
Class	2714b	Isogeny class
Conductor	2714	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	8832	Modular degree for the optimal curve
Δ	-911384434966528 = -1 · 223 · 232 · 593	Discriminant
Eigenvalues	2+  0 -2 -1  5  1  1 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-34628,2882896]	[a1,a2,a3,a4,a6]
Generators	[93:632:1]	Generators of the group modulo torsion
j	-4592117514716855577/911384434966528	j-invariant
L	2.1084618319242	L(r)(E,1)/r!
Ω	0.4770856601521	Real period
R	0.73657696022275	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21712e1 86848g1 24426j1 67850r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2714b1

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	-1	5	1	1	-2	-	-4	6	-1	-3	7	6	2	-	-2	-4	-3	0	9	-7	0	-18

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Quadratic twists for elliptic curve 2714b1

-4	8	-3	5	-23
21712e1	86848g1	24426j1	67850r1	62422c1

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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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