Cremona's table of elliptic curves

1692 = 2² · 3² · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 47-	Signs for the Atkin-Lehner involutions
Class	1692d	Isogeny class
Conductor	1692	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	236825856 = 28 · 39 · 47	Discriminant
Eigenvalues	2- 3-  3 -1  3 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-336,-2252]	[a1,a2,a3,a4,a6]
j	22478848/1269	j-invariant
L	2.2380580703512	L(r)(E,1)/r!
Ω	1.1190290351756	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6768q1 27072bh1 564b1 42300m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1692d1

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
-	-	3	-1	3	-4	0	2	9	3	-4	5	6	8	-	-6	-6	2	8	6	-4	-1	-6	6	-19

---

Quadratic twists for elliptic curve 1692d1

-4	8	-3	5	-7	-47
6768q1	27072bh1	564b1	42300m1	82908y1	79524j1

---

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