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	384	Product of Tamagawa factors cp
Δ	44772582831427584 = 212 · 38 · 78 · 172	Discriminant
Eigenvalues	2- 3+ -2 7-  4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-90724,2605541]	[a1,a2,a3,a4,a6]
j	82582985847542515777/44772582831427584	j-invariant
L	1.8827095166557	L(r)(E,1)/r!
Ω	0.31378491944262	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	5712t2 22848bn2 2142g2 17850o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714g2

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 714g2

-4	8	-3	5	-7	-11	13	17
5712t2	22848bn2	2142g2	17850o2	4998bm2	86394b2	120666d2	12138w2

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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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