# Properties

 Label 58800.gt Number of curves $2$ Conductor $58800$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58800.gt1")

sage: E.isogeny_class()

## Elliptic curves in class 58800.gt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.gt1 58800il1 [0, 1, 0, -294408, -23596812]  774144 $$\Gamma_0(N)$$-optimal
58800.gt2 58800il2 [0, 1, 0, 1077592, -180004812]  1548288

## Rank

sage: E.rank()

The elliptic curves in class 58800.gt have rank $$0$$.

## Modular form 58800.2.a.gt

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 2q^{11} + 2q^{13} - 4q^{17} + O(q^{20})$$

## 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. 