# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("90354.r1")

sage: E.isogeny_class()

## Elliptic curves in class 90354.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.r1 90354m2 [1, 1, 1, -157334, 23955059] [] 504000
90354.r2 90354m1 [1, 1, 1, 841, 8363] [] 100800 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 90354.2.a.r

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 