Cremona's table of elliptic curves

711 = 3² · 79

Field	Data	Notes
Atkin-Lehner	3+ 79+	Signs for the Atkin-Lehner involutions
Class	711b	Isogeny class
Conductor	711	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-1554957 = -1 · 39 · 79	Discriminant
Eigenvalues	-1 3+  0 -1  1 -3  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,25,28]	[a1,a2,a3,a4,a6]
Generators	[4:11:1]	Generators of the group modulo torsion
j	91125/79	j-invariant
L	1.4841485904609	L(r)(E,1)/r!
Ω	1.7397204637107	Real period
R	0.42654800625133	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	11376i1 45504b1 711a1 17775b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 711b1

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 711b1

-4	8	-3	5	-7	-11	13	-79
11376i1	45504b1	711a1	17775b1	34839b1	86031a1	120159a1	56169d1

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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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