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	1677b	Isogeny class
Conductor	1677	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-648999 = -1 · 33 · 13 · 432	Discriminant
Eigenvalues	-1 3-  2  0 -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-7,-40]	[a1,a2,a3,a4,a6]
Generators	[5:5:1]	Generators of the group modulo torsion
j	-38272753/648999	j-invariant
L	2.3869827518438	L(r)(E,1)/r!
Ω	1.2371304447319	Real period
R	1.2863007626551	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	26832k1 107328g1 5031d1 41925c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1677b1

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

---

Quadratic twists for elliptic curve 1677b1

-4	8	-3	5	-7	13	-43
26832k1	107328g1	5031d1	41925c1	82173e1	21801h1	72111b1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations