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	714a	Isogeny class
Conductor	714	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	352517816448 = 27 · 34 · 76 · 172	Discriminant
Eigenvalues	2+ 3+  2 7+ -6  0 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-55174,4965268]	[a1,a2,a3,a4,a6]
Generators	[49:1519:1]	Generators of the group modulo torsion
j	18575453384550358633/352517816448	j-invariant
L	1.5642040390478	L(r)(E,1)/r!
Ω	0.88148938851514	Real period
R	0.88725063479364	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	5712w2 22848x2 2142q2 17850cf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714a2

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

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Quadratic twists for elliptic curve 714a2

-4	8	-3	5	-7	-11	13	17
5712w2	22848x2	2142q2	17850cf2	4998w2	86394ci2	120666bp2	12138m2

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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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