# Properties

 Label 13860.v Number of curves $2$ Conductor $13860$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.v1 13860h2 $$[0, 0, 0, -927, -7786]$$ $$12745567728/3587045$$ $$24793655040$$ $$$$ $$10752$$ $$0.70146$$
13860.v2 13860h1 $$[0, 0, 0, -852, -9571]$$ $$158328373248/21175$$ $$9147600$$ $$$$ $$5376$$ $$0.35488$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 13860.v have rank $$1$$.

## Complex multiplication

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

## Modular form 13860.2.a.v

sage: E.q_eigenform(10)

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