# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("90354.i1")

sage: E.isogeny_class()

## Elliptic curves in class 90354.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.i1 90354g2 [1, 0, 1, -301348416, -2017081437554] [] 21098880
90354.i2 90354g1 [1, 0, 1, 6368559, -13696226156]  7032960 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 90354.2.a.i

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 