# Properties

 Label 141120.ni Number of curves $2$ Conductor $141120$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.ni1")

sage: E.isogeny_class()

## Elliptic curves in class 141120.ni

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ni1 141120jo1 [0, 0, 0, -8652, 118384] [2] 294912 $$\Gamma_0(N)$$-optimal
141120.ni2 141120jo2 [0, 0, 0, 31668, 908656] [2] 589824

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.ni

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.