Cremona's table of elliptic curves

1683 = 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	3+ 11+ 17+	Signs for the Atkin-Lehner involutions
Class	1683a	Isogeny class
Conductor	1683	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-813146499 = -1 · 33 · 116 · 17	Discriminant
Eigenvalues	1 3+  2 -2 11+ -2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,189,-988]	[a1,a2,a3,a4,a6]
Generators	[46:107:8]	Generators of the group modulo torsion
j	27570978261/30116537	j-invariant
L	3.5972318929792	L(r)(E,1)/r!
Ω	0.85844666835488	Real period
R	4.1903964749178	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	26928ba2 107712m2 1683d2 42075f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683a2

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	+	8	-4	-6	-8	-2	-6	-8	-6	0	6	-4	4	4	0	-6	16	-4	2

---

Quadratic twists for elliptic curve 1683a2

-4	8	-3	5	-7	-11	17
26928ba2	107712m2	1683d2	42075f2	82467c2	18513d2	28611d2

---

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