Cremona's table of elliptic curves

32368 = 2⁴ · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	32368q	Isogeny class
Conductor	32368	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-27610100615143424 = -1 · 213 · 79 · 174	Discriminant
Eigenvalues	2- -1  3 7+  0  5 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,13776,-7974848]	[a1,a2,a3,a4,a6]
Generators	[71280:1700104:125]	Generators of the group modulo torsion
j	845095823/80707214	j-invariant
L	5.8436904757687	L(r)(E,1)/r!
Ω	0.17783263898689	Real period
R	8.215154581662	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	4046r2 129472cl2 32368y2	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 32368q2

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
-	-1	3	+	0	5	-	4	-3	6	-2	-4	6	4	-6	-12	-12	-1	-8	9	-16	-8	3	6	-10

---

Quadratic twists for elliptic curve 32368q2

-4	8	17
4046r2	129472cl2	32368y2

---

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