Elliptic curve isogeny class with LMFDB label 164730.e (Cremona label 164730db)

• Label: 164730.e
• Number of curves: $2$
• Conductor: $164730$
• CM: no
• Rank: $1$

Elliptic curves in class 164730.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
164730.e1	164730db2	\([1, 1, 0, -18662903, 20842650453]\)	\(29782957153899582361/9454781800440000\)	\(228215448088064730360000\)	\([2]\)	\(21233664\)	\(3.1859\)
164730.e2	164730db1	\([1, 1, 0, -16905783, 26743410837]\)	\(22137883334842578841/4123121356800\)	\(99522126245133619200\)	\([2]\)	\(10616832\)	\(2.8393\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 164730.e have rank \(1\).

Complex multiplication

The elliptic curves in class 164730.e do not have complex multiplication.

Modular form 164730.2.a.e

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.