# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 58800.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.e1 58800gj2 $$[0, -1, 0, -59453, -5559903]$$ $$-30866268160/3$$ $$-2258860800$$ $$[]$$ $$163296$$ $$1.2282$$
58800.e2 58800gj1 $$[0, -1, 0, -653, -9183]$$ $$-40960/27$$ $$-20329747200$$ $$[]$$ $$54432$$ $$0.67887$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 58800.e do not have complex multiplication.

## Modular form 58800.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 6q^{11} + 5q^{13} - 6q^{17} + 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.