Cremona's table of elliptic curves

18240 = 2⁶ · 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	18240bw	Isogeny class
Conductor	18240	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-567803904000 = -1 · 222 · 3 · 53 · 192	Discriminant
Eigenvalues	2- 3+ 5+  2 -2  0 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1121,-38655]	[a1,a2,a3,a4,a6]
Generators	[976:30457:1]	Generators of the group modulo torsion
j	-594823321/2166000	j-invariant
L	4.1094534571466	L(r)(E,1)/r!
Ω	0.3780547631689	Real period
R	5.4349975949261	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	18240bc1 4560bb1 54720ex1 91200if1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18240bw1

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

---

Quadratic twists for elliptic curve 18240bw1

-4	8	-3	5
18240bc1	4560bb1	54720ex1	91200if1

---

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