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	714f	Isogeny class
Conductor	714	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	14438442312 = 23 · 32 · 74 · 174	Discriminant
Eigenvalues	2- 3+ -2 7+  0 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-679,-3883]	[a1,a2,a3,a4,a6]
Generators	[-19:60:1]	Generators of the group modulo torsion
j	34623662831857/14438442312	j-invariant
L	2.4625037273294	L(r)(E,1)/r!
Ω	0.97048615984086	Real period
R	0.21144932553986	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5712bb4 22848bc3 2142d4 17850s3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714f3

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	+	0	-6	-	0	-8	-6	-8	10	-6	12	0	-10	-8	6	12	0	-6	-8	16	2	2

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Quadratic twists for elliptic curve 714f3

-4	8	-3	5	-7	-11	13	17
5712bb4	22848bc3	2142d4	17850s3	4998bl4	86394l3	120666p3	12138ba3

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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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