# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.b1 13860i2 $$[0, 0, 0, -4863, 9718]$$ $$68150496976/39220335$$ $$7319455799040$$ $$$$ $$27648$$ $$1.1581$$
13860.b2 13860i1 $$[0, 0, 0, 1212, 1213]$$ $$16880451584/9823275$$ $$-114578679600$$ $$$$ $$13824$$ $$0.81148$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 13860.2.a.b

sage: E.q_eigenform(10)

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