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	770f	Isogeny class
Conductor	770	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	63690429687500 = 22 · 512 · 72 · 113	Discriminant
Eigenvalues	2- -2 5+ 7- 11+ -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-26116,-1580604]	[a1,a2,a3,a4,a6]
Generators	[-96:258:1]	Generators of the group modulo torsion
j	1969902499564819009/63690429687500	j-invariant
L	2.3511646469141	L(r)(E,1)/r!
Ω	0.37629901942862	Real period
R	3.1240642753789	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	6160g4 24640x4 6930p4 3850d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 770f4

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	+	-	+	-4	0	-4	0	-6	-10	2	-12	-4	6	-6	-6	-4	-4	12	-4	8	12	18	-10

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Quadratic twists for elliptic curve 770f4

-4	8	-3	5	-7	-11
6160g4	24640x4	6930p4	3850d4	5390bf4	8470f4

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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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