Elliptic curve isogeny class with LMFDB label 17424.v (Cremona label 17424bg)

• Label: 17424.v
• Number of curves: $2$
• Conductor: $17424$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 17424.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
17424.v1	17424bg1	\([0, 0, 0, 0, -1936]\)	\(0\)	\(-1619177472\)	\([]\)	\(8064\)	\(0.44598\)	\(\Gamma_0(N)\)-optimal	\(-3\)
17424.v2	17424bg2	\([0, 0, 0, 0, 52272]\)	\(0\)	\(-1180380377088\)	\([]\)	\(24192\)	\(0.99529\)		\(-3\)

Rank

The elliptic curves in class 17424.v have rank \(1\).

Complex multiplication

Each elliptic curve in class 17424.v has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 17424.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.