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	2112r	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	138412032 = 222 · 3 · 11	Discriminant
Eigenvalues	2+ 3- -2 -4 11-  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-129,-33]	[a1,a2,a3,a4,a6]
Generators	[-7:24:1]	Generators of the group modulo torsion
j	912673/528	j-invariant
L	3.0643337311967	L(r)(E,1)/r!
Ω	1.5587356244443	Real period
R	1.9659098586966	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	2112u1 66b1 6336o1 52800bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112r1

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

---

Quadratic twists for elliptic curve 2112r1

-4	8	-3	5	-7	-11
2112u1	66b1	6336o1	52800bj1	103488by1	23232cg1

---

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