Elliptic curve isogeny class with Cremona label 73920bk (LMFDB label 73920.dd)

• Label: 73920bk
• Number of curves: $4$
• Conductor: $73920$
• CM: no
• Rank: $1$

Elliptic curves in class 73920bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
73920.dd3	73920bk1	\([0, -1, 0, -63425, -4216383]\)	\(107639597521009/32699842560\)	\(8572067528048640\)	\([2]\)	\(491520\)	\(1.7623\)	\(\Gamma_0(N)\)-optimal
73920.dd2	73920bk2	\([0, -1, 0, -391105, 91007425]\)	\(25238585142450289/995844326400\)	\(261054615099801600\)	\([2, 2]\)	\(983040\)	\(2.1088\)
73920.dd4	73920bk3	\([0, -1, 0, 172095, 331043265]\)	\(2150235484224911/181905111732960\)	\(-47685333610125066240\)	\([2]\)	\(1966080\)	\(2.4554\)
73920.dd1	73920bk4	\([0, -1, 0, -6197185, 5940052417]\)	\(100407751863770656369/166028940000\)	\(43523490447360000\)	\([4]\)	\(1966080\)	\(2.4554\)

Rank

The elliptic curves in class 73920bk have rank \(1\).

Complex multiplication

The elliptic curves in class 73920bk do not have complex multiplication.

Modular form 73920.2.a.bk

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.