Elliptic curve isogeny class with Cremona label 494209i (LMFDB label 494209.i)

• Label: 494209i
• Number of curves: $2$
• Conductor: $494209$
• CM: \(\Q(\sqrt{-19}) \)
• Rank: $1$

Elliptic curves in class 494209i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
494209.i2	494209i1	\([0, 0, 1, -52022, 4571433]\)	\(-884736\)	\(-17598317439331\)	\([]\)	\(1039680\)	\(1.4553\)	\(\Gamma_0(N)\)-optimal	\(-19\)
494209.i1	494209i2	\([0, 0, 1, -18779942, -31355460662]\)	\(-884736\)	\(-827928348050990945611\)	\([]\)	\(19753920\)	\(2.9275\)		\(-19\)

Rank

The elliptic curves in class 494209i have rank \(1\).

Complex multiplication

Each elliptic curve in class 494209i has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).

Modular form 494209.2.a.i

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.