Elliptic curve isogeny class with Cremona label 442225bq (LMFDB label 442225.bq)

• Label: 442225bq
• Number of curves: $2$
• Conductor: $442225$
• CM: \(\Q(\sqrt{-19}) \)
• Rank: $0$

Elliptic curves in class 442225bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
442225.bq2	442225bq1	\([0, 0, 1, -46550, -3869469]\)	\(-884736\)	\(-12608663921875\)	\([]\)	\(924000\)	\(1.4275\)	\(\Gamma_0(N)\)-optimal^*	\(-19\)
442225.bq1	442225bq2	\([0, 0, 1, -16804550, 26540686156]\)	\(-884736\)	\(-593185702437524546875\)	\([]\)	\(17556000\)	\(2.8997\)	\(\Gamma_0(N)\)-optimal^*	\(-19\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 442225bq1.

Rank

The elliptic curves in class 442225bq have rank \(0\).

Complex multiplication

Each elliptic curve in class 442225bq has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).

Modular form 442225.2.a.bq

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.