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	16	Product of Tamagawa factors cp
Δ	-3100231750000 = -1 · 24 · 56 · 7 · 116	Discriminant
Eigenvalues	2- -2 5+ 7- 11+ -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,504,-84560]	[a1,a2,a3,a4,a6]
Generators	[58:346:1]	Generators of the group modulo torsion
j	14156681599871/3100231750000	j-invariant
L	2.3511646469141	L(r)(E,1)/r!
Ω	0.37629901942862	Real period
R	1.5620321376894	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	6160g3 24640x3 6930p3 3850d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 770f3

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 770f3

-4	8	-3	5	-7	-11
6160g3	24640x3	6930p3	3850d3	5390bf3	8470f3

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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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