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	714d	Isogeny class
Conductor	714	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1019592 = 23 · 32 · 72 · 172	Discriminant
Eigenvalues	2+ 3+ -2 7- -2  4 17- -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-381,2709]	[a1,a2,a3,a4,a6]
Generators	[9:6:1]	Generators of the group modulo torsion
j	6141556990297/1019592	j-invariant
L	1.3951533217234	L(r)(E,1)/r!
Ω	2.6839654335726	Real period
R	0.25990523280814	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	5712s2 22848bm2 2142r2 17850br2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714d2

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	-	-2	4	-	-2	-4	0	0	-8	-2	-4	0	-6	-10	-6	0	-8	-6	-12	6	6	14

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Quadratic twists for elliptic curve 714d2

-4	8	-3	5	-7	-11	13	17
5712s2	22848bm2	2142r2	17850br2	4998q2	86394bq2	120666bi2	12138h2

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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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