# Properties

 Label 141120.kf Number of curves $2$ Conductor $141120$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.kf1")

sage: E.isogeny_class()

## Elliptic curves in class 141120.kf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.kf1 141120p1 [0, 0, 0, -8652, -118384]  294912 $$\Gamma_0(N)$$-optimal
141120.kf2 141120p2 [0, 0, 0, 31668, -908656]  589824

## Rank

sage: E.rank()

The elliptic curves in class 141120.kf have rank $$1$$.

## Modular form 141120.2.a.kf

sage: E.q_eigenform(10)

$$q + q^{5} - 2q^{11} - 2q^{13} + 4q^{17} + O(q^{20})$$

## 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. 