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	2112b	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	1216512 = 212 · 33 · 11	Discriminant
Eigenvalues	2+ 3+  0  2 11+ -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-393,-2871]	[a1,a2,a3,a4,a6]
Generators	[25:48:1]	Generators of the group modulo torsion
j	1643032000/297	j-invariant
L	2.7305408928943	L(r)(E,1)/r!
Ω	1.0720476208405	Real period
R	2.547033209918	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	2112p1 1056j1 6336x1 52800ci1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112b1

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

---

Quadratic twists for elliptic curve 2112b1

-4	8	-3	5	-7	-11
2112p1	1056j1	6336x1	52800ci1	103488ct1	23232h1

---

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