Cremona's table of elliptic curves

6578 = 2 · 11 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 11+ 13- 23-	Signs for the Atkin-Lehner involutions
Class	6578d	Isogeny class
Conductor	6578	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	22464	Modular degree for the optimal curve
Δ	-72001419776 = -1 · 29 · 112 · 133 · 232	Discriminant
Eigenvalues	2- -3 -3 -3 11+ 13- -7 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2529,51249]	[a1,a2,a3,a4,a6]
Generators	[-57:116:1] [-39:318:1]	Generators of the group modulo torsion
j	-1788171617409633/72001419776	j-invariant
L	4.2010282955406	L(r)(E,1)/r!
Ω	1.0849401760719	Real period
R	0.035853046095798	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	52624i1 59202r1 72358c1 85514h1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 6578d1

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
-	-3	-3	-3	+	-	-7	-2	-	-6	-8	-3	-2	7	-7	-8	-12	-12	12	-13	-14	-2	-10	-4	10

---

Quadratic twists for elliptic curve 6578d1

-4	-3	-11	13
52624i1	59202r1	72358c1	85514h1

---

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