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	3	Product of Tamagawa factors cp
Δ	-244053849830826 = -1 · 2 · 3 · 73 · 179	Discriminant
Eigenvalues	2- 3- -3 7-  3  5 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-381702,-90803346]	[a1,a2,a3,a4,a6]
j	-6150311179917589675873/244053849830826	j-invariant
L	2.5929919851611	L(r)(E,1)/r!
Ω	0.096036740191153	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5712m3 22848o3 2142j3 17850e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714i3

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 714i3

-4	8	-3	5	-7	-11	13	17
5712m3	22848o3	2142j3	17850e3	4998bg3	86394bd3	120666t3	12138q3

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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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