Elliptic curve isogeny class with Cremona label 55440a (LMFDB label 55440.g)

• Label: 55440a
• Number of curves: $2$
• Conductor: $55440$
• CM: no
• Rank: $1$

Elliptic curves in class 55440a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55440.g2	55440a1	\([0, 0, 0, -12423, -544122]\)	\(-30676050095472/751953125\)	\(-5197500000000\)	\([2]\)	\(81920\)	\(1.2251\)	\(\Gamma_0(N)\)-optimal
55440.g1	55440a2	\([0, 0, 0, -199923, -34406622]\)	\(31963054227773868/18528125\)	\(512265600000\)	\([2]\)	\(163840\)	\(1.5717\)

Rank

The elliptic curves in class 55440a have rank \(1\).

Complex multiplication

The elliptic curves in class 55440a do not have complex multiplication.

Modular form 55440.2.a.a

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.