# Properties

 Label 141120pp Number of curves $4$ Conductor $141120$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.ek1")

sage: E.isogeny_class()

## Elliptic curves in class 141120pp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ek2 141120pp1 [0, 0, 0, -329868, -72831248]  884736 $$\Gamma_0(N)$$-optimal
141120.ek3 141120pp2 [0, 0, 0, -235788, -115242512]  1769472
141120.ek1 141120pp3 [0, 0, 0, -1317708, 510169968]  2654208
141120.ek4 141120pp4 [0, 0, 0, 2069172, 2700803952]  5308416

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.ek

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. 