Elliptic curve isogeny class with Cremona label 135240dq (LMFDB label 135240.n)

• Label: 135240dq
• Number of curves: $4$
• Conductor: $135240$
• CM: no
• Rank: $1$

Elliptic curves in class 135240dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
135240.n3	135240dq1	\([0, -1, 0, -144076, -20966924]\)	\(10981797946576/20708625\)	\(623705349792000\)	\([2]\)	\(1179648\)	\(1.7289\)	\(\Gamma_0(N)\)-optimal
135240.n2	135240dq2	\([0, -1, 0, -192096, -5734980]\)	\(6507178816324/3645140625\)	\(439139480976000000\)	\([2, 2]\)	\(2359296\)	\(2.0755\)
135240.n1	135240dq3	\([0, -1, 0, -1907096, 1008859020]\)	\(3183636045638162/19833730875\)	\(4778841300403968000\)	\([2]\)	\(4718592\)	\(2.4221\)
135240.n4	135240dq4	\([0, -1, 0, 754584, -46252884]\)	\(197209449637198/117919921875\)	\(-28412233500000000000\)	\([2]\)	\(4718592\)	\(2.4221\)

Rank

The elliptic curves in class 135240dq have rank \(1\).

Complex multiplication

The elliptic curves in class 135240dq do not have complex multiplication.

Modular form 135240.2.a.dq

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.