Cremona's table of elliptic curves

12240 = 2⁴ · 3² · 5 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 17-	Signs for the Atkin-Lehner involutions
Class	12240w	Isogeny class
Conductor	12240	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	-2974320 = -1 · 24 · 37 · 5 · 17	Discriminant
Eigenvalues	2+ 3- 5- -1  5  2 17-  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-147,-691]	[a1,a2,a3,a4,a6]
j	-30118144/255	j-invariant
L	2.7408216001437	L(r)(E,1)/r!
Ω	0.68520540003593	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6120x1 48960eu1 4080b1 61200bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240w1

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	5	2	-	1	-2	-9	10	9	3	-4	3	5	8	-14	-4	12	15	-10	12	-16	-10

---

Quadratic twists for elliptic curve 12240w1

-4	8	-3	5
6120x1	48960eu1	4080b1	61200bg1

---

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