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	2112a	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	2162688 = 216 · 3 · 11	Discriminant
Eigenvalues	2+ 3+  0  2 11+  0 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-33,33]	[a1,a2,a3,a4,a6]
Generators	[-1:8:1]	Generators of the group modulo torsion
j	62500/33	j-invariant
L	2.7503978874583	L(r)(E,1)/r!
Ω	2.2844315436097	Real period
R	1.2039747459941	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	2112ba1 264a1 6336w1 52800cf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112a1

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

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Quadratic twists for elliptic curve 2112a1

-4	8	-3	5	-7	-11
2112ba1	264a1	6336w1	52800cf1	103488cr1	23232g1

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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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