# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 13860.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.q1 13860t2 $$[0, 0, 0, -13042767, 18127933126]$$ $$1314817350433665559504/190690249278375$$ $$35587377081327456000$$ $$$$ $$645120$$ $$2.7665$$
13860.q2 13860t1 $$[0, 0, 0, -740892, 336961501]$$ $$-3856034557002072064/1973796785296875$$ $$-23022365703702750000$$ $$$$ $$322560$$ $$2.4199$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 13860.2.a.q

sage: E.q_eigenform(10)

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