Elliptic curve isogeny class with Cremona label 121968bl (LMFDB label 121968.z)

• Label: 121968bl
• Number of curves: $4$
• Conductor: $121968$
• CM: no
• Rank: $1$

Elliptic curves in class 121968bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121968.z4	121968bl1	\([0, 0, 0, 1089, -71874]\)	\(432/7\)	\(-2314310600448\)	\([2]\)	\(163840\)	\(1.0531\)	\(\Gamma_0(N)\)-optimal
121968.z3	121968bl2	\([0, 0, 0, -20691, -1078110]\)	\(740772/49\)	\(64800696812544\)	\([2, 2]\)	\(327680\)	\(1.3996\)
121968.z2	121968bl3	\([0, 0, 0, -64251, 4959306]\)	\(11090466/2401\)	\(6350468287629312\)	\([2]\)	\(655360\)	\(1.7462\)
121968.z1	121968bl4	\([0, 0, 0, -325611, -71514630]\)	\(1443468546/7\)	\(18514484803584\)	\([2]\)	\(655360\)	\(1.7462\)

Rank

The elliptic curves in class 121968bl have rank \(1\).

Complex multiplication

The elliptic curves in class 121968bl do not have complex multiplication.

Modular form 121968.2.a.bl

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.