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	777a	Isogeny class
Conductor	777	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	777 = 3 · 7 · 37	Discriminant
Eigenvalues	1 3+ -2 7+  4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-16,19]	[a1,a2,a3,a4,a6]
j	498677257/777	j-invariant
L	1.2599461386973	L(r)(E,1)/r!
Ω	5.0397845547893	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12432bz1 49728bk1 2331b1 19425u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 777a1

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

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Quadratic twists for elliptic curve 777a1

-4	8	-3	5	-7	-11	37
12432bz1	49728bk1	2331b1	19425u1	5439f1	94017l1	28749a1

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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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