# Properties

 Label 90354x Number of curves 2 Conductor 90354 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("90354.t1")

sage: E.isogeny_class()

## Elliptic curves in class 90354x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.t1 90354x1 [1, 0, 0, -50578418, 133339353924]  17335296 $$\Gamma_0(N)$$-optimal
90354.t2 90354x2 [1, 0, 0, 24388022, 494812534316]  34670592

## Rank

sage: E.rank()

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

## Modular form 90354.2.a.t

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 