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	714i	Isogeny class
Conductor	714	Conductor
∏ cp	81	Product of Tamagawa factors cp
Δ	-42823570577256 = -1 · 23 · 33 · 79 · 173	Discriminant
Eigenvalues	2- 3- -3 7-  3  5 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-972,-315144]	[a1,a2,a3,a4,a6]
j	-101566487155393/42823570577256	j-invariant
L	2.5929919851611	L(r)(E,1)/r!
Ω	0.28811022057346	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	5712m2 22848o2 2142j2 17850e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714i2

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
-	-	-3	-	3	5	+	2	6	-6	-4	11	-12	-1	12	-9	-12	-10	5	0	-7	-1	-15	9	-19

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Quadratic twists for elliptic curve 714i2

-4	8	-3	5	-7	-11	13	17
5712m2	22848o2	2142j2	17850e2	4998bg2	86394bd2	120666t2	12138q2

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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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