Elliptic curve isogeny class with LMFDB label 296450.r (Cremona label 296450r)

• Label: 296450.r
• Number of curves: $2$
• Conductor: $296450$
• CM: no
• Rank: $1$

Elliptic curves in class 296450.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
296450.r1	296450r2	\([1, 0, 1, -22146, -1269292]\)	\(553463785/512\)	\(1111123059200\)	\([]\)	\(933120\)	\(1.2345\)
296450.r2	296450r1	\([1, 0, 1, -971, 9678]\)	\(46585/8\)	\(17361297800\)	\([]\)	\(311040\)	\(0.68517\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 296450.r have rank \(1\).

Complex multiplication

The elliptic curves in class 296450.r do not have complex multiplication.

Modular form 296450.2.a.r

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.