# Properties

 Label 58800fp Number of curves $2$ Conductor $58800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58800.be1")

sage: E.isogeny_class()

## Elliptic curves in class 58800fp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.be1 58800fp1 [0, -1, 0, -6008, 70512] [2] 110592 $$\Gamma_0(N)$$-optimal
58800.be2 58800fp2 [0, -1, 0, 21992, 518512] [2] 221184

## Rank

sage: E.rank()

The elliptic curves in class 58800fp have rank $$1$$.

## Modular form 58800.2.a.be

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 Cremona 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 Cremona labels.