Cremona's table of elliptic curves

770 = 2 · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	770d	Isogeny class
Conductor	770	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-135520000 = -1 · 28 · 54 · 7 · 112	Discriminant
Eigenvalues	2+ -2 5- 7+ 11-  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,32,558]	[a1,a2,a3,a4,a6]
Generators	[4:25:1]	Generators of the group modulo torsion
j	3789119879/135520000	j-invariant
L	1.3476401146559	L(r)(E,1)/r!
Ω	1.3934589959707	Real period
R	0.24177965023598	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6160o1 24640c1 6930w1 3850u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 770d1

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	0	0	-4	2	-2	-6	8	-12	-6	-6	-10	-4	-8	-4	-4	-16	0	-6	14

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Quadratic twists for elliptic curve 770d1

-4	8	-3	5	-7	-11
6160o1	24640c1	6930w1	3850u1	5390j1	8470bg1

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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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