# Properties

 Label 13860.w Number of curves $2$ Conductor $13860$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.w1 13860w2 $$[0, 0, 0, -319287, 56253566]$$ $$19288565375865424/3837216796875$$ $$716116747500000000$$ $$$$ $$138240$$ $$2.1423$$
13860.w2 13860w1 $$[0, 0, 0, 41568, 5228669]$$ $$681010157060096/1406657896875$$ $$-16407257709150000$$ $$$$ $$69120$$ $$1.7957$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 13860.2.a.w

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + q^{11} + 2q^{13} - 2q^{17} + O(q^{20})$$ ## 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 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. 