# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.ir1")

sage: E.isogeny_class()

## Elliptic curves in class 141120d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ir4 141120d1 [0, 0, 0, 65268, 10224144] [2] 1179648 $$\Gamma_0(N)$$-optimal
141120.ir3 141120d2 [0, 0, 0, -499212, 109798416] [2, 2] 2359296
141120.ir1 141120d3 [0, 0, 0, -7555212, 7992761616] [2] 4718592
141120.ir2 141120d4 [0, 0, 0, -2474892, -1400411376] [2] 4718592

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.ir

sage: E.q_eigenform(10)

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

## 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.