# Properties

 Label 141120.cw Number of curves $2$ Conductor $141120$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.cw1")

sage: E.isogeny_class()

## Elliptic curves in class 141120.cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.cw1 141120do1 [0, 0, 0, -423948, 40605712]  2064384 $$\Gamma_0(N)$$-optimal
141120.cw2 141120do2 [0, 0, 0, 1551732, 311669008]  4128768

## Rank

sage: E.rank()

The elliptic curves in class 141120.cw have rank $$0$$.

## Modular form 141120.2.a.cw

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. 