Cremona's table of elliptic curves

83232 = 2⁵ · 3² · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+	Signs for the Atkin-Lehner involutions
Class	83232c	Isogeny class
Conductor	83232	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	66560	Modular degree for the optimal curve
Δ	-41709719232 = -1 · 26 · 33 · 176	Discriminant
Eigenvalues	2+ 3+  4  0  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,867,0]	[a1,a2,a3,a4,a6]
Generators	[605:8206:125]	Generators of the group modulo torsion
j	1728	j-invariant
L	8.656850929971	L(r)(E,1)/r!
Ω	0.68336454682288	Real period
R	6.3339918422697	Regulator
r	1	Rank of the group of rational points
S	1.0000000000261	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	83232c1 83232bb1 288a1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 83232c1

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
+	+	4	0	0	-6	+	0	0	-4	0	2	-8	0	0	4	0	10	0	0	-6	0	0	-16	18

---

Quadratic twists for elliptic curve 83232c1

-4	-3	17
83232c1	83232bb1	288a1

---

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