# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("dr1")

sage: E.isogeny_class()

## Elliptic curves in class 141120dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.dm3 141120dr1 [0, 0, 0, -71148, -6920368]  786432 $$\Gamma_0(N)$$-optimal
141120.dm2 141120dr2 [0, 0, 0, -212268, 29037008] [2, 2] 1572864
141120.dm1 141120dr3 [0, 0, 0, -3175788, 2178181712]  3145728
141120.dm4 141120dr4 [0, 0, 0, 493332, 181164368]  3145728

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 141120dr do not have complex multiplication.

## Modular form 141120.2.a.dr

sage: E.q_eigenform(10)

$$q - q^{5} - 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 