Cremona's table of elliptic curves

712 = 2³ · 89

Field	Data	Notes
Atkin-Lehner	2+ 89-	Signs for the Atkin-Lehner involutions
Class	712a	Isogeny class
Conductor	712	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	91136 = 210 · 89	Discriminant
Eigenvalues	2+ -2  2 -4  0  4  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-32,-80]	[a1,a2,a3,a4,a6]
j	3650692/89	j-invariant
L	1.0025412122671	L(r)(E,1)/r!
Ω	2.0050824245341	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	1424a1 5696f1 6408c1 17800m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 712a1

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

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Quadratic twists for elliptic curve 712a1

-4	8	-3	5	-7	-11	13	89
1424a1	5696f1	6408c1	17800m1	34888b1	86152d1	120328i1	63368a1

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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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