Elliptic curve isogeny class with LMFDB label 112710.ct (Cremona label 112710ck)

• Label: 112710.ct
• Number of curves: $2$
• Conductor: $112710$
• CM: no
• Rank: $1$

Elliptic curves in class 112710.ct

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
112710.ct1	112710ck1	\([1, 0, 0, -3936186, 2971212516]\)	\(279419703685750081/3666124800000\)	\(88491340322611200000\)	\([2]\)	\(4423680\)	\(2.6351\)	\(\Gamma_0(N)\)-optimal
112710.ct2	112710ck2	\([1, 0, 0, -606906, 7837954020]\)	\(-1024222994222401/1098922500000000\)	\(-26525317669402500000000\)	\([2]\)	\(8847360\)	\(2.9817\)

Rank

The elliptic curves in class 112710.ct have rank \(1\).

Complex multiplication

The elliptic curves in class 112710.ct do not have complex multiplication.

Modular form 112710.2.a.ct

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.