Elliptic curve isogeny class with Cremona label 10350o (LMFDB label 10350.n)

• Label: 10350o
• Number of curves: $4$
• Conductor: $10350$
• CM: no
• Rank: $1$

Elliptic curves in class 10350o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10350.n3	10350o1	\([1, -1, 0, -135792, 19215616]\)	\(24310870577209/114462720\)	\(1303801920000000\)	\([2]\)	\(92160\)	\(1.7500\)	\(\Gamma_0(N)\)-optimal
10350.n2	10350o2	\([1, -1, 0, -207792, -3320384]\)	\(87109155423289/49979073600\)	\(569292885225000000\)	\([2, 2]\)	\(184320\)	\(2.0966\)
10350.n1	10350o3	\([1, -1, 0, -2394792, -1422683384]\)	\(133345896593725369/340006815000\)	\(3872890127109375000\)	\([2]\)	\(368640\)	\(2.4432\)
10350.n4	10350o4	\([1, -1, 0, 827208, -27125384]\)	\(5495662324535111/3207841648920\)	\(-36539321282229375000\)	\([2]\)	\(368640\)	\(2.4432\)

Rank

The elliptic curves in class 10350o have rank \(1\).

Complex multiplication

The elliptic curves in class 10350o do not have complex multiplication.

Modular form 10350.2.a.o

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.