# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("90354.d1")

sage: E.isogeny_class()

## Elliptic curves in class 90354.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.d1 90354d2 [1, 1, 0, -6382494330, -196446593263212] [] 131580288
90354.d2 90354d1 [1, 1, 0, 8394680, 101611095184] [] 18797184 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 90354.2.a.d

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 