# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("fa1")

sage: E.isogeny_class()

## Elliptic curves in class 58800fa

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.j2 58800fa1 $$[0, -1, 0, -20008, -2505488]$$ $$-2401/6$$ $$-2213683584000000$$ $$[]$$ $$282240$$ $$1.6323$$ $$\Gamma_0(N)$$-optimal
58800.j1 58800fa2 $$[0, -1, 0, -2764008, 1835974512]$$ $$-6329617441/279936$$ $$-103281621295104000000$$ $$[]$$ $$1975680$$ $$2.6053$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 58800.2.a.fa

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 5q^{11} + 4q^{17} - 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 