Cremona's table of elliptic curves

42432 = 2⁶ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 17+	Signs for the Atkin-Lehner involutions
Class	42432z	Isogeny class
Conductor	42432	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	331776	Modular degree for the optimal curve
Δ	-679048132336704 = -1 · 26 · 32 · 132 · 178	Discriminant
Eigenvalues	2+ 3-  2  2 -2 13- 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-361912,83690510]	[a1,a2,a3,a4,a6]
Generators	[-275450126:1624901055:405224]	Generators of the group modulo torsion
j	-81913199224986275392/10610127067761	j-invariant
L	9.1680832562595	L(r)(E,1)/r!
Ω	0.49130797107878	Real period
R	9.3302814079351	Regulator
r	1	Rank of the group of rational points
S	1.0000000000007	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42432f1 21216i2 127296bp1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 42432z1

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	-2	-	+	-2	8	6	-10	-2	-10	-8	6	-6	6	-6	-10	10	2	-4	-6	-10	2

---

Quadratic twists for elliptic curve 42432z1

-4	8	-3
42432f1	21216i2	127296bp1

---

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