Elliptic curve isogeny class with LMFDB label 133570.v (Cremona label 133570k)

• Label: 133570.v
• Number of curves: $3$
• Conductor: $133570$
• CM: no
• Rank: $1$

Elliptic curves in class 133570.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
133570.v1	133570k1	\([1, 1, 1, -19321, -1041767]\)	\(-16954786009/370\)	\(-17406975970\)	\([]\)	\(256608\)	\(1.0810\)	\(\Gamma_0(N)\)-optimal
133570.v2	133570k2	\([1, 1, 1, -6686, -2360861]\)	\(-702595369/50653000\)	\(-2383015010293000\)	\([]\)	\(769824\)	\(1.6303\)
133570.v3	133570k3	\([1, 1, 1, 60099, 63248723]\)	\(510273943271/37000000000\)	\(-1740697597000000000\)	\([]\)	\(2309472\)	\(2.1796\)

Rank

The elliptic curves in class 133570.v have rank \(1\).

Complex multiplication

The elliptic curves in class 133570.v do not have complex multiplication.

Modular form 133570.2.a.v

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.