# Properties

 Label 141120gg Number of curves $4$ Conductor $141120$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.mg1")

sage: E.isogeny_class()

## Elliptic curves in class 141120gg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.mg3 141120gg1 [0, 0, 0, -146412, 18895184] [2] 884736 $$\Gamma_0(N)$$-optimal
141120.mg4 141120gg2 [0, 0, 0, 229908, 100029776] [2] 1769472
141120.mg1 141120gg3 [0, 0, 0, -2968812, -1966443696] [2] 2654208
141120.mg2 141120gg4 [0, 0, 0, -2122092, -3111547824] [2] 5308416

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.mg

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.