Cremona's table of elliptic curves

1748 = 2² · 19 · 23

Field	Data	Notes
Atkin-Lehner	2- 19- 23+	Signs for the Atkin-Lehner involutions
Class	1748f	Isogeny class
Conductor	1748	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-928873216 = -1 · 28 · 193 · 232	Discriminant
Eigenvalues	2- -2 -3 -1  3  2  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-157,1599]	[a1,a2,a3,a4,a6]
Generators	[-11:46:1]	Generators of the group modulo torsion
j	-1682464768/3628411	j-invariant
L	1.7568190782039	L(r)(E,1)/r!
Ω	1.3958499752493	Real period
R	0.62930082363976	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	6992l1 27968b1 15732i1 43700l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1748f1

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
-	-2	-3	-1	3	2	3	-	+	0	-4	-4	12	11	-9	-12	0	-7	-4	0	-7	-10	12	6	-10

---

Quadratic twists for elliptic curve 1748f1

-4	8	-3	5	-7	-19	-23
6992l1	27968b1	15732i1	43700l1	85652b1	33212c1	40204d1

---

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