Cremona's table of elliptic curves

714 = 2 · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	714i	Isogeny class
Conductor	714	Conductor
∏ cp	243	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	-58763045376 = -1 · 29 · 39 · 73 · 17	Discriminant
Eigenvalues	2- 3- -3 7-  3  5 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,108,11664]	[a1,a2,a3,a4,a6]
j	139233463487/58763045376	j-invariant
L	2.5929919851611	L(r)(E,1)/r!
Ω	0.86433066172037	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	9	Number of elements in the torsion subgroup
Twists	5712m1 22848o1 2142j1 17850e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714i1

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
-	-	-3	-	3	5	+	2	6	-6	-4	11	-12	-1	12	-9	-12	-10	5	0	-7	-1	-15	9	-19

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Quadratic twists for elliptic curve 714i1

-4	8	-3	5	-7	-11	13	17
5712m1	22848o1	2142j1	17850e1	4998bg1	86394bd1	120666t1	12138q1

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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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