# Properties

 Label 90354j Number of curves 4 Conductor 90354 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("90354.g1")

sage: E.isogeny_class()

## Elliptic curves in class 90354j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.g4 90354j1 [1, 0, 1, -2105551, 431193986]  4727808 $$\Gamma_0(N)$$-optimal
90354.g3 90354j2 [1, 0, 1, -18314511, -29866594046]  9455616
90354.g2 90354j3 [1, 0, 1, -92459551, -342192619678]  14183424
90354.g1 90354j4 [1, 0, 1, -1479338691, -21900396723494]  28366848

## Rank

sage: E.rank()

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

## Modular form 90354.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 