Elliptic curve isogeny class with Cremona label 54150bc (LMFDB label 54150.bi)

• Label: 54150bc
• Number of curves: $4$
• Conductor: $54150$
• CM: no
• Rank: $1$

Elliptic curves in class 54150bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54150.bi4	54150bc1	\([1, 0, 1, 112624, 12690398]\)	\(214921799/218880\)	\(-160896913020000000\)	\([2]\)	\(1105920\)	\(1.9885\)	\(\Gamma_0(N)\)-optimal
54150.bi3	54150bc2	\([1, 0, 1, -609376, 116658398]\)	\(34043726521/11696400\)	\(8597928789506250000\)	\([2, 2]\)	\(2211840\)	\(2.3351\)
54150.bi2	54150bc3	\([1, 0, 1, -4038876, -3038481602]\)	\(9912050027641/311647500\)	\(229089549983554687500\)	\([2]\)	\(4423680\)	\(2.6816\)
54150.bi1	54150bc4	\([1, 0, 1, -8731876, 9928638398]\)	\(100162392144121/23457780\)	\(17243623850065312500\)	\([2]\)	\(4423680\)	\(2.6816\)

Rank

The elliptic curves in class 54150bc have rank \(1\).

Complex multiplication

The elliptic curves in class 54150bc do not have complex multiplication.

Modular form 54150.2.a.bc

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.