# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("90354.q1")

sage: E.isogeny_class()

## Elliptic curves in class 90354.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.q1 90354p1 [1, 1, 1, -652357, -201137401]  1838592 $$\Gamma_0(N)$$-optimal
90354.q2 90354p2 [1, 1, 1, -145827, -504852789]  3677184

## Rank

sage: E.rank()

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

## Modular form 90354.2.a.q

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + 2q^{7} + q^{8} + q^{9} + 2q^{10} + q^{11} - q^{12} + 6q^{13} + 2q^{14} - 2q^{15} + q^{16} + 2q^{17} + q^{18} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 