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	4	Product of Tamagawa factors cp
Δ	216333 = 32 · 13 · 432	Discriminant
Eigenvalues	-1 3+  2  2 -2 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-72,204]	[a1,a2,a3,a4,a6]
Generators	[-6:24:1]	Generators of the group modulo torsion
j	41314084993/216333	j-invariant
L	1.8592432380844	L(r)(E,1)/r!
Ω	3.1716280697543	Real period
R	0.5862109923338	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	26832r2 107328bf2 5031c2 41925m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1677a2

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 1677a2

-4	8	-3	5	-7	13	-43
26832r2	107328bf2	5031c2	41925m2	82173k2	21801b2	72111d2

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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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