# Properties

 Label 108900ct Number of curves $4$ Conductor $108900$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 108900ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
108900.f4 108900ct1 [0, 0, 0, -1234200, 516927125]  2488320 $$\Gamma_0(N)$$-optimal
108900.f3 108900ct2 [0, 0, 0, -2731575, -981945250]  4976640
108900.f2 108900ct3 [0, 0, 0, -12124200, -16044040375]  7464960
108900.f1 108900ct4 [0, 0, 0, -193306575, -1034470170250]  14929920

## Rank

sage: E.rank()

The elliptic curves in class 108900ct have rank $$0$$.

## Complex multiplication

The elliptic curves in class 108900ct do not have complex multiplication.

## Modular form 108900.2.a.ct

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 