Elliptic curve isogeny class with Cremona label 25230k (LMFDB label 25230.n)

• Label: 25230k
• Number of curves: $4$
• Conductor: $25230$
• CM: no
• Rank: $1$

Elliptic curves in class 25230k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25230.n3	25230k1	\([1, 0, 1, -210268, 37037978]\)	\(1728432036001/3006720\)	\(1788467175717120\)	\([2]\)	\(215040\)	\(1.8204\)	\(\Gamma_0(N)\)-optimal
25230.n2	25230k2	\([1, 0, 1, -277548, 11310106]\)	\(3975097468321/2207120400\)	\(1312846686174848400\)	\([2, 2]\)	\(430080\)	\(2.1670\)
25230.n4	25230k3	\([1, 0, 1, 1084872, 89785498]\)	\(237395127814559/143224402500\)	\(-85193214743290702500\)	\([2]\)	\(860160\)	\(2.5135\)
25230.n1	25230k4	\([1, 0, 1, -2716448, -1713479974]\)	\(3726830856733921/24967098180\)	\(14851012255160655780\)	\([2]\)	\(860160\)	\(2.5135\)

Rank

The elliptic curves in class 25230k have rank \(1\).

Complex multiplication

The elliptic curves in class 25230k do not have complex multiplication.

Modular form 25230.2.a.k

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.