# Properties

 Label 108900.x Number of curves 2 Conductor 108900 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("108900.x1")

sage: E.isogeny_class()

## Elliptic curves in class 108900.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
108900.x1 108900cf2 [0, 0, 0, -335775, -35604250]  1474560
108900.x2 108900cf1 [0, 0, 0, 72600, -4159375]  737280 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 108900.x have rank $$2$$.

## Modular form 108900.2.a.x

sage: E.q_eigenform(10)

$$q - 2q^{7} - 2q^{13} - 4q^{17} + 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 