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	24	Product of Tamagawa factors cp
Δ	-2.0992495115465E+20	Discriminant
Eigenvalues	2- 3+ -2 7-  4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-292604,-699871003]	[a1,a2,a3,a4,a6]
j	-2770540998624539614657/209924951154647363208	j-invariant
L	1.8827095166557	L(r)(E,1)/r!
Ω	0.078446229860655	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5712t6 22848bn5 2142g6 17850o6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714g6

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 714g6

-4	8	-3	5	-7	-11	13	17
5712t6	22848bn5	2142g6	17850o6	4998bm6	86394b5	120666d5	12138w6

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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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