Cremona's table of elliptic curves

2288 = 2⁴ · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	2288i	Isogeny class
Conductor	2288	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-7614464 = -1 · 212 · 11 · 132	Discriminant
Eigenvalues	2-  1 -1  2 11- 13+ -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21,131]	[a1,a2,a3,a4,a6]
Generators	[-2:13:1]	Generators of the group modulo torsion
j	-262144/1859	j-invariant
L	3.512871774612	L(r)(E,1)/r!
Ω	2.0157723238708	Real period
R	0.87134636511587	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	143a1 9152v1 20592bb1 57200bx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2288i1

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	-1	2	-	+	-4	-2	-7	-2	3	-11	10	4	4	2	1	-2	1	9	-16	-8	0	-7	-13

---

Quadratic twists for elliptic curve 2288i1

-4	8	-3	5	-7	-11	13
143a1	9152v1	20592bb1	57200bx1	112112bt1	25168bh1	29744m1

---

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