# Properties

 Label 90354.e Number of curves 4 Conductor 90354 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("90354.e1")

sage: E.isogeny_class()

## Elliptic curves in class 90354.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.e1 90354b4 [1, 1, 0, -482064, 84967680]  2304000
90354.e2 90354b2 [1, 1, 0, -191799, -32410935]  460800
90354.e3 90354b1 [1, 1, 0, -11979, -510867]  230400 $$\Gamma_0(N)$$-optimal
90354.e4 90354b3 [1, 1, 0, 86256, 9153792]  1152000

## Rank

sage: E.rank()

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

## Modular form 90354.2.a.e

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 