# Properties

 Label 141120mu Number of curves $6$ Conductor $141120$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.gv1")

sage: E.isogeny_class()

## Elliptic curves in class 141120mu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.gv6 141120mu1 [0, 0, 0, 281652, -80514448] [2] 2359296 $$\Gamma_0(N)$$-optimal
141120.gv5 141120mu2 [0, 0, 0, -1976268, -832853392] [2, 2] 4718592
141120.gv4 141120mu3 [0, 0, 0, -10443468, 12277759088] [2] 9437184
141120.gv2 141120mu4 [0, 0, 0, -29635788, -62093158288] [2, 2] 9437184
141120.gv3 141120mu5 [0, 0, 0, -27660108, -70728460432] [2] 18874368
141120.gv1 141120mu6 [0, 0, 0, -474163788, -3974117369488] [2] 18874368

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.gv

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{11} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.