Elliptic curve isogeny class with Cremona label 27200cm (LMFDB label 27200.j)

• Label: 27200cm
• Number of curves: $2$
• Conductor: $27200$
• CM: no
• Rank: $1$

Elliptic curves in class 27200cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27200.j2	27200cm1	\([0, 1, 0, -833, 6463]\)	\(62500/17\)	\(17408000000\)	\([2]\)	\(18432\)	\(0.67287\)	\(\Gamma_0(N)\)-optimal
27200.j1	27200cm2	\([0, 1, 0, -4833, -125537]\)	\(6097250/289\)	\(591872000000\)	\([2]\)	\(36864\)	\(1.0194\)

Rank

The elliptic curves in class 27200cm have rank \(1\).

Complex multiplication

The elliptic curves in class 27200cm do not have complex multiplication.

Modular form 27200.2.a.cm

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.