Cremona's table of elliptic curves

54600 = 2³ · 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	54600x	Isogeny class
Conductor	54600	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	14607684000000 = 28 · 32 · 56 · 74 · 132	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21308,-1190112]	[a1,a2,a3,a4,a6]
Generators	[259:3276:1]	Generators of the group modulo torsion
j	267492843088/3651921	j-invariant
L	8.0604261897761	L(r)(E,1)/r!
Ω	0.39547683424787	Real period
R	2.547692270371	Regulator
r	1	Rank of the group of rational points
S	0.99999999999793	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	109200b2 2184h2	Quadratic twists by: -4 5

Hecke Eigenvalues for elliptic curve 54600x2

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
+	-	+	-	0	+	6	-4	0	-2	-8	-6	6	-4	12	2	0	-2	12	4	-10	-16	0	-2	-2

---

Quadratic twists for elliptic curve 54600x2

-4	5
109200b2	2184h2

---

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