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	552468975892674624 = 26 · 316 · 74 · 174	Discriminant
Eigenvalues	2- 3+ -2 7-  4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-859044,-304722459]	[a1,a2,a3,a4,a6]
j	70108386184777836280897/552468975892674624	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	5712t3 22848bn4 2142g3 17850o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714g3

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 714g3

-4	8	-3	5	-7	-11	13	17
5712t3	22848bn4	2142g3	17850o3	4998bm3	86394b4	120666d4	12138w3

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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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