Elliptic curve isogeny class with Cremona label 37440dz (LMFDB label 37440.cp)

• Label: 37440dz
• Number of curves: $4$
• Conductor: $37440$
• CM: no
• Rank: $1$

Elliptic curves in class 37440dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37440.cp3	37440dz1	\([0, 0, 0, -4008, 97432]\)	\(9538484224/26325\)	\(19651507200\)	\([2]\)	\(49152\)	\(0.84805\)	\(\Gamma_0(N)\)-optimal
37440.cp2	37440dz2	\([0, 0, 0, -5628, 11248]\)	\(1650587344/950625\)	\(11354204160000\)	\([2, 2]\)	\(98304\)	\(1.1946\)
37440.cp4	37440dz3	\([0, 0, 0, 22452, 89872]\)	\(26198797244/15234375\)	\(-727833600000000\)	\([2]\)	\(196608\)	\(1.5412\)
37440.cp1	37440dz4	\([0, 0, 0, -59628, -5583152]\)	\(490757540836/2142075\)	\(102339226828800\)	\([2]\)	\(196608\)	\(1.5412\)

Rank

The elliptic curves in class 37440dz have rank \(1\).

Complex multiplication

The elliptic curves in class 37440dz do not have complex multiplication.

Modular form 37440.2.a.dz

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.