Cremona's table of elliptic curves

711 = 3² · 79

Field	Data	Notes
Atkin-Lehner	3+ 79+	Signs for the Atkin-Lehner involutions
Class	711a	Isogeny class
Conductor	711	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-2133 = -1 · 33 · 79	Discriminant
Eigenvalues	1 3+  0 -1 -1 -3 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,3,-2]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	91125/79	j-invariant
L	2.5771593912078	L(r)(E,1)/r!
Ω	2.5535933872098	Real period
R	0.50461428278207	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11376h1 45504a1 711b1 17775e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 711a1

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	+	0	-1	-1	-3	-3	-2	1	-3	-4	-2	10	-5	-4	10	0	-4	2	6	-1	+	9	-8	-1

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Quadratic twists for elliptic curve 711a1

-4	8	-3	5	-7	-11	13	-79
11376h1	45504a1	711b1	17775e1	34839a1	86031b1	120159c1	56169c1

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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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