Cremona's table of elliptic curves

6358 = 2 · 11 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 11+ 17+	Signs for the Atkin-Lehner involutions
Class	6358a	Isogeny class
Conductor	6358	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	47736	Modular degree for the optimal curve
Δ	-21466303051980952 = -1 · 23 · 113 · 1710	Discriminant
Eigenvalues	2+  2  0 -2 11+  5 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-43500,-7884856]	[a1,a2,a3,a4,a6]
Generators	[2399345959549427:25880716808785565:7266438420409]	Generators of the group modulo torsion
j	-4515625/10648	j-invariant
L	3.9988460761088	L(r)(E,1)/r!
Ω	0.15432201010506	Real period
R	25.912350891403	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	50864bq1 57222bp1 69938o1 6358g1	Quadratic twists by: -4 -3 -11 17

Hecke Eigenvalues for elliptic curve 6358a1

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	0	-2	+	5	+	-1	3	-3	-5	10	0	-4	-3	-6	-12	-14	-4	0	-2	10	9	-6	-2

---

Quadratic twists for elliptic curve 6358a1

-4	-3	-11	17
50864bq1	57222bp1	69938o1	6358g1

---

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