Elliptic curve isogeny class with Cremona label 102850ce (LMFDB label 102850.di)

• Label: 102850ce
• Number of curves: $4$
• Conductor: $102850$
• CM: no
• Rank: $1$

Elliptic curves in class 102850ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
102850.di4	102850ce1	\([1, 1, 1, -9138, -211969]\)	\(3048625/1088\)	\(30116537000000\)	\([2]\)	\(311040\)	\(1.2873\)	\(\Gamma_0(N)\)-optimal
102850.di3	102850ce2	\([1, 1, 1, -130138, -18119969]\)	\(8805624625/2312\)	\(63997641125000\)	\([2]\)	\(622080\)	\(1.6338\)
102850.di2	102850ce3	\([1, 1, 1, -311638, 66822031]\)	\(120920208625/19652\)	\(543979949562500\)	\([2]\)	\(933120\)	\(1.8366\)
102850.di1	102850ce4	\([1, 1, 1, -341888, 53028031]\)	\(159661140625/48275138\)	\(1336286746100281250\)	\([2]\)	\(1866240\)	\(2.1832\)

Rank

The elliptic curves in class 102850ce have rank \(1\).

Complex multiplication

The elliptic curves in class 102850ce do not have complex multiplication.

Modular form 102850.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.