# Properties

 Label 141120en Number of curves $6$ Conductor $141120$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.gx1")

sage: E.isogeny_class()

## Elliptic curves in class 141120en

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.gx4 141120en1 [0, 0, 0, -309288, -66204488] [2] 786432 $$\Gamma_0(N)$$-optimal
141120.gx3 141120en2 [0, 0, 0, -318108, -62228432] [2, 2] 1572864
141120.gx2 141120en3 [0, 0, 0, -1200108, 439100368] [2, 2] 3145728
141120.gx5 141120en4 [0, 0, 0, 422772, -309089648] [2] 3145728
141120.gx1 141120en5 [0, 0, 0, -18487308, 30594892048] [2] 6291456
141120.gx6 141120en6 [0, 0, 0, 1975092, 2368351888] [2] 6291456

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.gx

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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.