Cremona's table of elliptic curves

2112 = 2⁶ · 3 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11-	Signs for the Atkin-Lehner involutions
Class	2112j	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	1576599552 = 216 · 37 · 11	Discriminant
Eigenvalues	2+ 3+ -4 -2 11-  0 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-32065,-2199359]	[a1,a2,a3,a4,a6]
j	55635379958596/24057	j-invariant
L	0.3567718876556	L(r)(E,1)/r!
Ω	0.3567718876556	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2112z1 264d1 6336u1 52800cx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112j1

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

---

Quadratic twists for elliptic curve 2112j1

-4	8	-3	5	-7	-11
2112z1	264d1	6336u1	52800cx1	103488el1	23232be1

---

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