# Properties

 Label 13923l Number of curves $2$ Conductor $13923$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 13923l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13923.k1 13923l1 $$[1, -1, 0, -4095, -99792]$$ $$10418796526321/6390657$$ $$4658788953$$ $$[2]$$ $$17920$$ $$0.79795$$ $$\Gamma_0(N)$$-optimal
13923.k2 13923l2 $$[1, -1, 0, -3330, -138807]$$ $$-5602762882081/8312741073$$ $$-6059988242217$$ $$[2]$$ $$35840$$ $$1.1445$$

## Rank

sage: E.rank()

The elliptic curves in class 13923l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 13923l do not have complex multiplication.

## Modular form 13923.2.a.l

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + 4q^{5} + q^{7} - 3q^{8} + 4q^{10} + 4q^{11} + q^{13} + q^{14} - q^{16} - q^{17} + O(q^{20})$$

## 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.