# Properties

 Label 90354v Number of curves 4 Conductor 90354 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("90354.x1")

sage: E.isogeny_class()

## Elliptic curves in class 90354v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.x3 90354v1 [1, 0, 0, -7558, 237920] [2] 193536 $$\Gamma_0(N)$$-optimal
90354.x4 90354v2 [1, 0, 0, 6132, 1007298] [2] 387072
90354.x1 90354v3 [1, 0, 0, -110233, -14042119] [2] 580608
90354.x2 90354v4 [1, 0, 0, -55473, -27984015] [2] 1161216

## Rank

sage: E.rank()

The elliptic curves in class 90354v have rank $$1$$.

## Modular form 90354.2.a.x

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} + q^{8} + q^{9} - q^{11} + q^{12} + 4q^{13} + 2q^{14} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.