Elliptic curve isogeny class with LMFDB label 393129.bl (Cremona label 393129bl)

• Label: 393129.bl
• Number of curves: $2$
• Conductor: $393129$
• CM: \(\Q(\sqrt{-19}) \)
• Rank: $1$

Elliptic curves in class 393129.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
393129.bl1	393129bl2	\([0, 0, 1, -14938902, -22245892441]\)	\(-884736\)	\(-416740825671930940851\)	\([]\)	\(14470400\)	\(2.8703\)		\(-19\)
393129.bl2	393129bl1	\([0, 0, 1, -41382, 3243314]\)	\(-884736\)	\(-8858178799371\)	\([]\)	\(761600\)	\(1.3981\)	\(\Gamma_0(N)\)-optimal	\(-19\)

Rank

The elliptic curves in class 393129.bl have rank \(1\).

Complex multiplication

Each elliptic curve in class 393129.bl has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).

Modular form 393129.2.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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.