Cremona's table of elliptic curves

777 = 3 · 7 · 37

Field	Data	Notes
Atkin-Lehner	3+ 7- 37-	Signs for the Atkin-Lehner involutions
Class	777d	Isogeny class
Conductor	777	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-266511 = -1 · 3 · 74 · 37	Discriminant
Eigenvalues	-1 3+ -2 7-  0  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-14,26]	[a1,a2,a3,a4,a6]
Generators	[4:5:1]	Generators of the group modulo torsion
j	-304821217/266511	j-invariant
L	1.2399116896979	L(r)(E,1)/r!
Ω	2.8360196315228	Real period
R	1.7488055102526	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12432bs1 49728cf1 2331h1 19425n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 777d1

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

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Quadratic twists for elliptic curve 777d1

-4	8	-3	5	-7	-11	37
12432bs1	49728cf1	2331h1	19425n1	5439h1	94017f1	28749d1

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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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