Cremona's table of elliptic curves

708 = 2² · 3 · 59

Field	Data	Notes
Atkin-Lehner	2- 3+ 59+	Signs for the Atkin-Lehner involutions
Class	708a	Isogeny class
Conductor	708	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	90	Modular degree for the optimal curve
Δ	-688176 = -1 · 24 · 36 · 59	Discriminant
Eigenvalues	2- 3+ -2  0 -4  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,11,34]	[a1,a2,a3,a4,a6]
j	8388608/43011	j-invariant
L	1.0309773001688	L(r)(E,1)/r!
Ω	2.0619546003376	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2832f1 11328h1 2124b1 17700l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 708a1

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

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Quadratic twists for elliptic curve 708a1

-4	8	-3	5	-7	-11	13	-59
2832f1	11328h1	2124b1	17700l1	34692s1	85668c1	119652b1	41772c1

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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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