# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fv1")

sage: E.isogeny_class()

## Elliptic curves in class 58800fv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.s2 58800fv1 $$[0, -1, 0, 460192, -147525888]$$ $$596183/864$$ $$-15619751368704000000$$ $$[]$$ $$1088640$$ $$2.3684$$ $$\Gamma_0(N)$$-optimal
58800.s1 58800fv2 $$[0, -1, 0, -13945808, -20143053888]$$ $$-16591834777/98304$$ $$-1777180600172544000000$$ $$[]$$ $$3265920$$ $$2.9177$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 58800.2.a.fv

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 3q^{11} - 4q^{13} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.