Elliptic curve isogeny class with Cremona label 23104x (LMFDB label 23104.z)

• Label: 23104x
• Number of curves: $2$
• Conductor: $23104$
• CM: \(\Q(\sqrt{-19}) \)
• Rank: $2$

Elliptic curves in class 23104x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
23104.z2	23104x1	\([0, 0, 0, -152, -722]\)	\(-884736\)	\(-438976\)	\([]\)	\(2880\)	\(-0.0035751\)	\(\Gamma_0(N)\)-optimal	\(-19\)
23104.z1	23104x2	\([0, 0, 0, -54872, 4952198]\)	\(-884736\)	\(-20652012657856\)	\([]\)	\(54720\)	\(1.4686\)		\(-19\)

Rank

The elliptic curves in class 23104x have rank \(2\).

Complex multiplication

Each elliptic curve in class 23104x has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).

Modular form 23104.2.a.x

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.