Cremona's table of elliptic curves

1424 = 2⁴ · 89

Field	Data	Notes
Atkin-Lehner	2+ 89-	Signs for the Atkin-Lehner involutions
Class	1424a	Isogeny class
Conductor	1424	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	91136 = 210 · 89	Discriminant
Eigenvalues	2+  2  2  4  0  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-32,80]	[a1,a2,a3,a4,a6]
j	3650692/89	j-invariant
L	3.383732816577	L(r)(E,1)/r!
Ω	3.383732816577	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	712a1 5696p1 12816b1 35600k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1424a1

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	2	4	0	4	2	-2	-4	-8	-4	8	6	-10	-8	-2	2	4	8	-8	-2	-8	-10	-	14

---

Quadratic twists for elliptic curve 1424a1

-4	8	-3	5	-7	89
712a1	5696p1	12816b1	35600k1	69776c1	126736c1

---

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