# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.e1 13860l2 $$[0, 0, 0, -16383, -777418]$$ $$2605772594896/108945375$$ $$20331821664000$$ $$$$ $$27648$$ $$1.3185$$
13860.e2 13860l1 $$[0, 0, 0, 492, -45043]$$ $$1129201664/75796875$$ $$-884094750000$$ $$$$ $$13824$$ $$0.97190$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 13860.2.a.e

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. 