# Properties

 Label 13860.d Number of curves $2$ Conductor $13860$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.d1 13860k2 $$[0, 0, 0, -423, -2322]$$ $$44851536/13475$$ $$2514758400$$ $$[2]$$ $$6144$$ $$0.50907$$
13860.d2 13860k1 $$[0, 0, 0, 72, -243]$$ $$3538944/4235$$ $$-49397040$$ $$[2]$$ $$3072$$ $$0.16250$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 13860.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 13860.d do not have complex multiplication.

## Modular form 13860.2.a.d

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} + q^{11} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.