# Properties

 Label 141120cb Number of curves $4$ Conductor $141120$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 141120cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ov3 141120cb1 [0, 0, 0, -99372, 7611856] [2] 1179648 $$\Gamma_0(N)$$-optimal
141120.ov2 141120cb2 [0, 0, 0, -663852, -202600496] [2, 2] 2359296
141120.ov4 141120cb3 [0, 0, 0, 182868, -683876144] [2] 4718592
141120.ov1 141120cb4 [0, 0, 0, -10542252, -13174915376] [2] 4718592

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 141120cb do not have complex multiplication.

## Modular form 141120.2.a.cb

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.