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	714c	Isogeny class
Conductor	714	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	2040	Modular degree for the optimal curve
Δ	-1011143540736 = -1 · 217 · 33 · 75 · 17	Discriminant
Eigenvalues	2+ 3+  1 7-  5 -1 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-14597,-686643]	[a1,a2,a3,a4,a6]
j	-344002044213921241/1011143540736	j-invariant
L	1.0856587496694	L(r)(E,1)/r!
Ω	0.21713174993388	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	5712q1 22848bg1 2142s1 17850bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714c1

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
+	+	1	-	5	-1	+	-6	6	6	4	11	0	-9	4	-7	12	6	13	4	-13	15	13	13	-9

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Quadratic twists for elliptic curve 714c1

-4	8	-3	5	-7	-11	13	17
5712q1	22848bg1	2142s1	17850bt1	4998u1	86394bt1	120666bf1	12138g1

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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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