Cremona's table of elliptic curves

2448 = 2⁴ · 3² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 17-	Signs for the Atkin-Lehner involutions
Class	2448f	Isogeny class
Conductor	2448	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	12690432 = 210 · 36 · 17	Discriminant
Eigenvalues	2+ 3-  0  0  2 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-75,-182]	[a1,a2,a3,a4,a6]
Generators	[-3:4:1]	Generators of the group modulo torsion
j	62500/17	j-invariant
L	3.1821476547633	L(r)(E,1)/r!
Ω	1.6554143003705	Real period
R	0.96113331087304	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	1224d1 9792bu1 272a1 61200ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2448f1

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	0	2	-6	-	-4	4	0	8	-4	-6	-8	-8	-10	0	12	-8	12	2	4	16	-10	-18

---

Quadratic twists for elliptic curve 2448f1

-4	8	-3	5	-7	17
1224d1	9792bu1	272a1	61200ba1	119952t1	41616o1

---

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