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	2112s	Isogeny class
Conductor	2112	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-32845824 = -1 · 212 · 36 · 11	Discriminant
Eigenvalues	2- 3+  2 -2 11+  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,23,265]	[a1,a2,a3,a4,a6]
j	314432/8019	j-invariant
L	1.5585254592129	L(r)(E,1)/r!
Ω	1.5585254592129	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	2112bb2 1056f1 6336cj2 52800ga2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112s2

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

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Quadratic twists for elliptic curve 2112s2

-4	8	-3	5	-7	-11
2112bb2	1056f1	6336cj2	52800ga2	103488hv2	23232da2

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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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