# Properties

 Label 22050.d Number of curves $2$ Conductor $22050$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 22050.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.d1 22050bv2 $$[1, -1, 0, -3864492, -3092833584]$$ $$-7620530425/526848$$ $$-441266692545000000000$$ $$[]$$ $$1244160$$ $$2.7123$$
22050.d2 22050bv1 $$[1, -1, 0, 269883, -4455459]$$ $$2595575/1512$$ $$-1266390380390625000$$ $$[]$$ $$414720$$ $$2.1630$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 22050.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 22050.d do not have complex multiplication.

## Modular form 22050.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 6q^{11} - q^{13} + q^{16} - 3q^{17} + 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.