# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.n1 13860d1 $$[0, 0, 0, -48, 117]$$ $$28311552/2695$$ $$1164240$$ $$$$ $$2688$$ $$-0.098164$$ $$\Gamma_0(N)$$-optimal
13860.n2 13860d2 $$[0, 0, 0, 57, 558]$$ $$2963088/21175$$ $$-146361600$$ $$$$ $$5376$$ $$0.24841$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 13860.2.a.n

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + q^{11} + 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 