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
Δ	24060672 = 28 · 33 · 592	Discriminant
Eigenvalues	2- 3+ -2  0 -4  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-124,520]	[a1,a2,a3,a4,a6]
j	830321872/93987	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	2832f2 11328h2 2124b2 17700l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 708a2

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 708a2

-4	8	-3	5	-7	-11	13	-59
2832f2	11328h2	2124b2	17700l2	34692s2	85668c2	119652b2	41772c2

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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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