# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.y1")

sage: E.isogeny_class()

## Elliptic curves in class 141120lh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.y4 141120lh1 [0, 0, 0, -309288, 66204488] [2] 786432 $$\Gamma_0(N)$$-optimal
141120.y3 141120lh2 [0, 0, 0, -318108, 62228432] [2, 2] 1572864
141120.y5 141120lh3 [0, 0, 0, 422772, 309089648] [2] 3145728
141120.y2 141120lh4 [0, 0, 0, -1200108, -439100368] [2, 2] 3145728
141120.y6 141120lh5 [0, 0, 0, 1975092, -2368351888] [2] 6291456
141120.y1 141120lh6 [0, 0, 0, -18487308, -30594892048] [2] 6291456

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.y

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.