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	2288f	Isogeny class
Conductor	2288	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-13592294144 = -1 · 28 · 11 · 136	Discriminant
Eigenvalues	2- -1  3 -2 11+ 13-  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1669,27401]	[a1,a2,a3,a4,a6]
Generators	[25:26:1]	Generators of the group modulo torsion
j	-2009615368192/53094899	j-invariant
L	2.9307210990531	L(r)(E,1)/r!
Ω	1.2534289002054	Real period
R	0.19484691809356	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	572a2 9152z2 20592bx2 57200y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2288f2

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	3	-2	+	-	0	-2	3	-6	1	-7	6	-8	-12	-6	-9	2	7	3	8	4	12	-15	-13

---

Quadratic twists for elliptic curve 2288f2

-4	8	-3	5	-7	-11	13
572a2	9152z2	20592bx2	57200y2	112112bb2	25168ba2	29744bb2

---

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