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	714g	Isogeny class
Conductor	714	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	-2928751705237796928 = -1 · 26 · 34 · 716 · 17	Discriminant
Eigenvalues	2- 3+ -2 7-  4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,349916,20936165]	[a1,a2,a3,a4,a6]
j	4738217997934888496063/2928751705237796928	j-invariant
L	1.8827095166557	L(r)(E,1)/r!
Ω	0.15689245972131	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5712t4 22848bn3 2142g4 17850o4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714g4

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

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Quadratic twists for elliptic curve 714g4

-4	8	-3	5	-7	-11	13	17
5712t4	22848bn3	2142g4	17850o4	4998bm4	86394b3	120666d3	12138w4

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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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