Elliptic curve isogeny class with LMFDB label 88445.w (Cremona label 88445bn)

• Label: 88445.w
• Number of curves: $3$
• Conductor: $88445$
• CM: no
• Rank: $2$

Elliptic curves in class 88445.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
88445.w1	88445bn3	\([0, 1, 1, -2323155, -1426494191]\)	\(-250523582464/13671875\)	\(-75672472610123046875\)	\([]\)	\(2052864\)	\(2.5726\)
88445.w2	88445bn1	\([0, 1, 1, -23585, 1538779]\)	\(-262144/35\)	\(-193721529881915\)	\([]\)	\(228096\)	\(1.4740\)	\(\Gamma_0(N)\)-optimal
88445.w3	88445bn2	\([0, 1, 1, 153305, -3891744]\)	\(71991296/42875\)	\(-237308874105345875\)	\([]\)	\(684288\)	\(2.0233\)

Rank

The elliptic curves in class 88445.w have rank \(2\).

Complex multiplication

The elliptic curves in class 88445.w do not have complex multiplication.

Modular form 88445.2.a.w

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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.