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	12240v	Isogeny class
Conductor	12240	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	-83652750000000000 = -1 · 210 · 39 · 512 · 17	Discriminant
Eigenvalues	2+ 3- 5-  0 -4  6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,41253,-13536614]	[a1,a2,a3,a4,a6]
j	10400706415004/112060546875	j-invariant
L	2.0185618469827	L(r)(E,1)/r!
Ω	0.16821348724856	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6120m4 48960er3 4080l4 61200bd3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240v4

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	-4	6	-	-4	-8	6	-4	2	-6	4	4	-10	12	6	4	0	14	4	16	-10	6

---

Quadratic twists for elliptic curve 12240v4

-4	8	-3	5
6120m4	48960er3	4080l4	61200bd3

---

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