# Properties

 Label 90354h Number of curves 2 Conductor 90354 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("90354.h1")

sage: E.isogeny_class()

## Elliptic curves in class 90354h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.h2 90354h1 [1, 0, 1, 36934, -1478464]  447552 $$\Gamma_0(N)$$-optimal
90354.h1 90354h2 [1, 0, 1, -722861, -240965848] [] 1342656

## Rank

sage: E.rank()

The elliptic curves in class 90354h have rank $$0$$.

## Modular form 90354.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - q^{11} + q^{12} - 4q^{13} + q^{14} + q^{16} - 3q^{17} - q^{18} + 5q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 