Elliptic curve isogeny class with Cremona label 67270m (LMFDB label 67270.e)

• Label: 67270m
• Number of curves: $2$
• Conductor: $67270$
• CM: no
• Rank: $1$

Elliptic curves in class 67270m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
67270.e2	67270m1	\([1, 0, 1, -9243, -344794]\)	\(-2930960362231/20070400\)	\(-597917286400\)	\([2]\)	\(143360\)	\(1.0940\)	\(\Gamma_0(N)\)-optimal
67270.e1	67270m2	\([1, 0, 1, -148123, -21954522]\)	\(12064294055330551/560000\)	\(16682960000\)	\([2]\)	\(286720\)	\(1.4406\)

Rank

The elliptic curves in class 67270m have rank \(1\).

Complex multiplication

The elliptic curves in class 67270m do not have complex multiplication.

Modular form 67270.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.