Elliptic curve isogeny class with Cremona label 2112f (LMFDB label 2112.l)

• Label: 2112f
• Number of curves: $4$
• Conductor: $2112$
• CM: no
• Rank: $0$

Elliptic curves in class 2112f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2112.l3	2112f1	\([0, -1, 0, -132, 630]\)	\(4004529472/99\)	\(6336\)	\([2]\)	\(256\)	\(-0.16135\)	\(\Gamma_0(N)\)-optimal
2112.l2	2112f2	\([0, -1, 0, -137, 585]\)	\(69934528/9801\)	\(40144896\)	\([2, 2]\)	\(512\)	\(0.18522\)
2112.l1	2112f3	\([0, -1, 0, -577, -4607]\)	\(649461896/72171\)	\(2364899328\)	\([2]\)	\(1024\)	\(0.53179\)
2112.l4	2112f4	\([0, -1, 0, 223, 2817]\)	\(37259704/131769\)	\(-4317806592\)	\([4]\)	\(1024\)	\(0.53179\)

Rank

The elliptic curves in class 2112f have rank \(0\).

Complex multiplication

The elliptic curves in class 2112f do not have complex multiplication.

Modular form 2112.2.a.f

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.