Elliptic curve isogeny class with LMFDB label 127296.r (Cremona label 127296dr)

• Label: 127296.r
• Number of curves: $2$
• Conductor: $127296$
• CM: no
• Rank: $1$

Elliptic curves in class 127296.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
127296.r1	127296dr2	\([0, 0, 0, -5196, -143440]\)	\(649461896/3757\)	\(89746735104\)	\([2]\)	\(122880\)	\(0.94265\)
127296.r2	127296dr1	\([0, 0, 0, -516, 704]\)	\(5088448/2873\)	\(8578732032\)	\([2]\)	\(61440\)	\(0.59607\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 127296.r have rank \(1\).

Complex multiplication

The elliptic curves in class 127296.r do not have complex multiplication.

Modular form 127296.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.