# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("90354.c1")

sage: E.isogeny_class()

## Elliptic curves in class 90354a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.c4 90354a1 [1, 1, 0, -2766, -156]  202752 $$\Gamma_0(N)$$-optimal
90354.c2 90354a2 [1, 1, 0, -30146, -2020800] [2, 2] 405504
90354.c3 90354a3 [1, 1, 0, -16456, -3847046]  811008
90354.c1 90354a4 [1, 1, 0, -481916, -128968170]  811008

## Rank

sage: E.rank()

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

## Modular form 90354.2.a.c

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 