Elliptic curve isogeny class with LMFDB label 111573.r (Cremona label 111573j)

• Label: 111573.r
• Number of curves: $2$
• Conductor: $111573$
• CM: no
• Rank: $1$

Elliptic curves in class 111573.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
111573.r1	111573j1	\([1, -1, 1, -104, -374]\)	\(13312053/253\)	\(2343033\)	\([2]\)	\(16896\)	\(0.015672\)	\(\Gamma_0(N)\)-optimal
111573.r2	111573j2	\([1, -1, 1, 1, -1172]\)	\(27/64009\)	\(-592787349\)	\([2]\)	\(33792\)	\(0.36225\)

Rank

The elliptic curves in class 111573.r have rank \(1\).

Complex multiplication

The elliptic curves in class 111573.r do not have complex multiplication.

Modular form 111573.2.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.