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.