Cremona's table of elliptic curves

58176 = 2⁶ · 3² · 101

Field	Data	Notes
Atkin-Lehner	2+ 3+ 101+	Signs for the Atkin-Lehner involutions
Class	58176a	Isogeny class
Conductor	58176	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	-5718933504 = -1 · 221 · 33 · 101	Discriminant
Eigenvalues	2+ 3+ -1 -2  4  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-108,-3664]	[a1,a2,a3,a4,a6]
Generators	[70:576:1]	Generators of the group modulo torsion
j	-19683/808	j-invariant
L	5.8489487582103	L(r)(E,1)/r!
Ω	0.59025114440113	Real period
R	1.2386568018057	Regulator
r	1	Rank of the group of rational points
S	0.99999999998663	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	58176bm1 1818j1 58176d1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 58176a1

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	-2	4	2	-6	8	2	2	9	2	-5	2	2	-8	-14	-7	7	8	-10	3	-4	-5	-13

---

Quadratic twists for elliptic curve 58176a1

-4	8	-3
58176bm1	1818j1	58176d1

---

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