Elliptic curve isogeny class with Cremona label 12992bl (LMFDB label 12992.bi)

• Label: 12992bl
• Number of curves: $2$
• Conductor: $12992$
• CM: no
• Rank: $0$

Elliptic curves in class 12992bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12992.bi1	12992bl1	\([0, -1, 0, -29, 29]\)	\(2725888/1421\)	\(1455104\)	\([2]\)	\(1792\)	\(-0.12560\)	\(\Gamma_0(N)\)-optimal
12992.bi2	12992bl2	\([0, -1, 0, 111, 113]\)	\(9148592/5887\)	\(-96452608\)	\([2]\)	\(3584\)	\(0.22097\)

Rank

The elliptic curves in class 12992bl have rank \(0\).

Complex multiplication

The elliptic curves in class 12992bl do not have complex multiplication.

Modular form 12992.2.a.bl

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.