Elliptic curve isogeny class with Cremona label 291312bm (LMFDB label 291312.bm)

• Label: 291312bm
• Number of curves: $2$
• Conductor: $291312$
• CM: no
• Rank: $1$

Elliptic curves in class 291312bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
291312.bm2	291312bm1	\([0, 0, 0, -15606, 1193859]\)	\(-55296/49\)	\(-372478220171568\)	\([2]\)	\(884736\)	\(1.4930\)	\(\Gamma_0(N)\)-optimal
291312.bm1	291312bm2	\([0, 0, 0, -288711, 59692950]\)	\(21882096/7\)	\(851378788963584\)	\([2]\)	\(1769472\)	\(1.8396\)

Rank

The elliptic curves in class 291312bm have rank \(1\).

Complex multiplication

The elliptic curves in class 291312bm do not have complex multiplication.

Modular form 291312.2.a.bm

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.