Elliptic curve isogeny class with Cremona label 22050bc (LMFDB label 22050.bn)

• Label: 22050bc
• Number of curves: $2$
• Conductor: $22050$
• CM: no
• Rank: $1$

Elliptic curves in class 22050bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22050.bn2	22050bc1	\([1, -1, 0, -72, 216]\)	\(46585/8\)	\(7144200\)	\([]\)	\(5184\)	\(0.035525\)	\(\Gamma_0(N)\)-optimal
22050.bn1	22050bc2	\([1, -1, 0, -1647, -25299]\)	\(553463785/512\)	\(457228800\)	\([]\)	\(15552\)	\(0.58483\)

Rank

The elliptic curves in class 22050bc have rank \(1\).

Complex multiplication

The elliptic curves in class 22050bc do not have complex multiplication.

Modular form 22050.2.a.bc

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.