Elliptic curve isogeny class with LMFDB label 165649.g (Cremona label 165649g)

• Label: 165649.g
• Number of curves: $2$
• Conductor: $165649$
• CM: \(\Q(\sqrt{-11}) \)
• Rank: $1$

Elliptic curves in class 165649.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
165649.g1	165649g2	\([0, -1, 1, -1214759, -528335952]\)	\(-32768\)	\(-6049848661839271619\)	\([]\)	\(2209680\)	\(2.3813\)		\(-11\)
165649.g2	165649g1	\([0, -1, 1, -10039, 400597]\)	\(-32768\)	\(-3414981850379\)	\([]\)	\(200880\)	\(1.1824\)	\(\Gamma_0(N)\)-optimal	\(-11\)

Rank

The elliptic curves in class 165649.g have rank \(1\).

Complex multiplication

Each elliptic curve in class 165649.g has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 165649.2.a.g

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.