Cremona's table of elliptic curves

1677 = 3 · 13 · 43

Field	Data	Notes
Atkin-Lehner	3+ 13+ 43+	Signs for the Atkin-Lehner involutions
Class	1677a	Isogeny class
Conductor	1677	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	21801 = 3 · 132 · 43	Discriminant
Eigenvalues	-1 3+  2  2 -2 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-7,-4]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	38272753/21801	j-invariant
L	1.8592432380844	L(r)(E,1)/r!
Ω	3.1716280697543	Real period
R	1.1724219846676	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	26832r1 107328bf1 5031c1 41925m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1677a1

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

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Quadratic twists for elliptic curve 1677a1

-4	8	-3	5	-7	13	-43
26832r1	107328bf1	5031c1	41925m1	82173k1	21801b1	72111d1

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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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