Elliptic curve isogeny class with Cremona label 132600ce (LMFDB label 132600.b)

• Label: 132600ce
• Number of curves: $4$
• Conductor: $132600$
• CM: no
• Rank: $1$

Elliptic curves in class 132600ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
132600.b4	132600ce1	\([0, -1, 0, -262783, -10485188]\)	\(8027441608013824/4452347908125\)	\(1113086977031250000\)	\([2]\)	\(2359296\)	\(2.1532\)	\(\Gamma_0(N)\)-optimal
132600.b2	132600ce2	\([0, -1, 0, -3188908, -2187522188]\)	\(896581610757188944/1545359765625\)	\(6181439062500000000\)	\([2, 2]\)	\(4718592\)	\(2.4998\)
132600.b3	132600ce3	\([0, -1, 0, -2194408, -3577833188]\)	\(-73039208963041156/303497314453125\)	\(-4855957031250000000000\)	\([2]\)	\(9437184\)	\(2.8464\)
132600.b1	132600ce4	\([0, -1, 0, -51001408, -140174397188]\)	\(916959671620739147236/2731145625\)	\(43698330000000000\)	\([2]\)	\(9437184\)	\(2.8464\)

Rank

The elliptic curves in class 132600ce have rank \(1\).

Complex multiplication

The elliptic curves in class 132600ce do not have complex multiplication.

Modular form 132600.2.a.ce

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.