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	2112q	Isogeny class
Conductor	2112	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-665127936 = -1 · 210 · 310 · 11	Discriminant
Eigenvalues	2+ 3- -2  2 11- -6 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-309,2331]	[a1,a2,a3,a4,a6]
Generators	[6:27:1]	Generators of the group modulo torsion
j	-3196715008/649539	j-invariant
L	3.3353309750469	L(r)(E,1)/r!
Ω	1.547777855368	Real period
R	0.43098316253581	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	2112t1 132b1 6336m1 52800bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112q1

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	2	-	-6	-4	2	-8	0	0	6	0	-10	0	-14	12	14	-4	0	6	2	-16	-14	-2

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Quadratic twists for elliptic curve 2112q1

-4	8	-3	5	-7	-11
2112t1	132b1	6336m1	52800bf1	103488bx1	23232ce1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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