Elliptic curve isogeny class with Cremona label 136367m (LMFDB label 136367.m)

• Label: 136367m
• Number of curves: $4$
• Conductor: $136367$
• CM: no
• Rank: $1$

Elliptic curves in class 136367m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
136367.m3	136367m1	\([1, -1, 0, -21863, -1207200]\)	\(5545233/161\)	\(33556003194329\)	\([2]\)	\(307200\)	\(1.3731\)	\(\Gamma_0(N)\)-optimal
136367.m2	136367m2	\([1, -1, 0, -51508, 2794875]\)	\(72511713/25921\)	\(5402516514286969\)	\([2, 2]\)	\(614400\)	\(1.7197\)
136367.m1	136367m3	\([1, -1, 0, -733343, 241846226]\)	\(209267191953/55223\)	\(11509709095654847\)	\([2]\)	\(1228800\)	\(2.0663\)
136367.m4	136367m4	\([1, -1, 0, 156007, 19520584]\)	\(2014698447/1958887\)	\(-408275890865400943\)	\([2]\)	\(1228800\)	\(2.0663\)

Rank

The elliptic curves in class 136367m have rank \(1\).

Complex multiplication

The elliptic curves in class 136367m do not have complex multiplication.

Modular form 136367.2.a.m

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.