Elliptic curve isogeny class with Cremona label 12992h (LMFDB label 12992.d)

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

Elliptic curves in class 12992h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12992.d1	12992h1	\([0, 1, 0, -29, -29]\)	\(2725888/1421\)	\(1455104\)	\([2]\)	\(1792\)	\(-0.12560\)	\(\Gamma_0(N)\)-optimal
12992.d2	12992h2	\([0, 1, 0, 111, -113]\)	\(9148592/5887\)	\(-96452608\)	\([2]\)	\(3584\)	\(0.22097\)

Rank

The elliptic curves in class 12992h have rank \(2\).

Complex multiplication

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

Modular form 12992.2.a.h

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.