# Properties

 Label 141120.mh Number of curves $4$ Conductor $141120$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.mh1")

sage: E.isogeny_class()

## Elliptic curves in class 141120.mh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.mh1 141120oh3 [0, 0, 0, -2968812, 1966443696]  2654208
141120.mh2 141120oh4 [0, 0, 0, -2122092, 3111547824]  5308416
141120.mh3 141120oh1 [0, 0, 0, -146412, -18895184]  884736 $$\Gamma_0(N)$$-optimal
141120.mh4 141120oh2 [0, 0, 0, 229908, -100029776]  1769472

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.mh

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 LMFDB 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 LMFDB labels. 