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	1748d	Isogeny class
Conductor	1748	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-1361146624 = -1 · 28 · 19 · 234	Discriminant
Eigenvalues	2- -2  3  1  1 -4 -7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-389,3319]	[a1,a2,a3,a4,a6]
Generators	[10:23:1]	Generators of the group modulo torsion
j	-25494618112/5316979	j-invariant
L	2.519905451474	L(r)(E,1)/r!
Ω	1.457040310124	Real period
R	0.43236714762879	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6992q1 27968s1 15732e1 43700c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1748d1

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	1	-4	-7	+	-	-6	-4	-10	2	5	-1	-4	-2	7	8	6	17	0	-12	12	-16

---

Quadratic twists for elliptic curve 1748d1

-4	8	-3	5	-7	-19	-23
6992q1	27968s1	15732e1	43700c1	85652k1	33212f1	40204l1

---

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