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	714h	Isogeny class
Conductor	714	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-714 = -1 · 2 · 3 · 7 · 17	Discriminant
Eigenvalues	2- 3+  3 7- -1  3 17- -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1,-1]	[a1,a2,a3,a4,a6]
j	103823/714	j-invariant
L	2.5311266382228	L(r)(E,1)/r!
Ω	2.5311266382228	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5712u1 22848bp1 2142i1 17850n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714h1

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	-	-1	3	-	-6	-2	6	0	3	0	11	0	-9	-4	-14	-7	12	-1	-5	3	-1	-13

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Quadratic twists for elliptic curve 714h1

-4	8	-3	5	-7	-11	13	17
5712u1	22848bp1	2142i1	17850n1	4998bo1	86394c1	120666e1	12138x1

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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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