Elliptic curve isogeny class with Cremona label 26450o (LMFDB label 26450.q)

• Label: 26450o
• Number of curves: $4$
• Conductor: $26450$
• CM: no
• Rank: $1$

Elliptic curves in class 26450o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26450.q3	26450o1	\([1, 1, 1, -1598, -30309]\)	\(-121945/32\)	\(-118428711200\)	\([]\)	\(23760\)	\(0.84165\)	\(\Gamma_0(N)\)-optimal
26450.q4	26450o2	\([1, 1, 1, 11627, 223611]\)	\(46969655/32768\)	\(-121271000268800\)	\([]\)	\(71280\)	\(1.3910\)
26450.q2	26450o3	\([1, 1, 1, -6888, 2593531]\)	\(-25/2\)	\(-2891325957031250\)	\([]\)	\(118800\)	\(1.6464\)
26450.q1	26450o4	\([1, 1, 1, -1660013, 822543531]\)	\(-349938025/8\)	\(-11565303828125000\)	\([]\)	\(356400\)	\(2.1957\)

Rank

The elliptic curves in class 26450o have rank \(1\).

Complex multiplication

The elliptic curves in class 26450o do not have complex multiplication.

Modular form 26450.2.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.

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.