Elliptic curve isogeny class with LMFDB label 129600.hk (Cremona label 129600iv)

• Label: 129600.hk
• Number of curves: $4$
• Conductor: $129600$
• CM: no
• Rank: $1$

Elliptic curves in class 129600.hk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129600.hk1	129600iv3	\([0, 0, 0, -1723500, -870894000]\)	\(-189613868625/128\)	\(-382205952000000\)	\([]\)	\(1161216\)	\(2.1138\)
129600.hk2	129600iv4	\([0, 0, 0, -1363500, -1244862000]\)	\(-1159088625/2097152\)	\(-507227047723008000000\)	\([]\)	\(3483648\)	\(2.6631\)
129600.hk3	129600iv2	\([0, 0, 0, -67500, 7074000]\)	\(-140625/8\)	\(-1934917632000000\)	\([]\)	\(497664\)	\(1.6902\)
129600.hk4	129600iv1	\([0, 0, 0, 4500, 18000]\)	\(3375/2\)	\(-5971968000000\)	\([]\)	\(165888\)	\(1.1409\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 129600.hk have rank \(1\).

Complex multiplication

The elliptic curves in class 129600.hk do not have complex multiplication.

Modular form 129600.2.a.hk

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.