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	6	Product of Tamagawa factors cp
Δ	6246072 = 23 · 38 · 7 · 17	Discriminant
Eigenvalues	2- 3+ -2 7+  0 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5079,137205]	[a1,a2,a3,a4,a6]
Generators	[41:-18:1]	Generators of the group modulo torsion
j	14489843500598257/6246072	j-invariant
L	2.4625037273294	L(r)(E,1)/r!
Ω	1.9409723196817	Real period
R	0.84579730215942	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	5712bb3 22848bc4 2142d3 17850s4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714f4

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 714f4

-4	8	-3	5	-7	-11	13	17
5712bb3	22848bc4	2142d3	17850s4	4998bl3	86394l4	120666p4	12138ba4

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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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