Elliptic curve isogeny class with Cremona label 193200ed (LMFDB label 193200.db)

• Label: 193200ed
• Number of curves: $4$
• Conductor: $193200$
• CM: no
• Rank: $1$

Elliptic curves in class 193200ed

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
193200.db4	193200ed1	\([0, -1, 0, 11592, 1107312]\)	\(2691419471/9891840\)	\(-633077760000000\)	\([2]\)	\(884736\)	\(1.5230\)	\(\Gamma_0(N)\)-optimal
193200.db3	193200ed2	\([0, -1, 0, -116408, 13395312]\)	\(2725812332209/373262400\)	\(23888793600000000\)	\([2, 2]\)	\(1769472\)	\(1.8696\)
193200.db1	193200ed3	\([0, -1, 0, -1796408, 927315312]\)	\(10017490085065009/235066440\)	\(15044252160000000\)	\([2]\)	\(3538944\)	\(2.2162\)
193200.db2	193200ed4	\([0, -1, 0, -484408, -116140688]\)	\(196416765680689/22365315000\)	\(1431380160000000000\)	\([2]\)	\(3538944\)	\(2.2162\)

Rank

The elliptic curves in class 193200ed have rank \(1\).

Complex multiplication

The elliptic curves in class 193200ed do not have complex multiplication.

Modular form 193200.2.a.ed

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.