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
deg	3840	Modular degree for the optimal curve
Δ	55468445663232 = 224 · 34 · 74 · 17	Discriminant
Eigenvalues	2- 3+ -2 7-  4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-70244,7127525]	[a1,a2,a3,a4,a6]
j	38331145780597164097/55468445663232	j-invariant
L	1.8827095166557	L(r)(E,1)/r!
Ω	0.62756983888524	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	5712t1 22848bn1 2142g1 17850o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714g1

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 714g1

-4	8	-3	5	-7	-11	13	17
5712t1	22848bn1	2142g1	17850o1	4998bm1	86394b1	120666d1	12138w1

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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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