# Properties

 Label 141120mh Number of curves $2$ Conductor $141120$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.fs1")

sage: E.isogeny_class()

## Elliptic curves in class 141120mh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.fs1 141120mh1 [0, 0, 0, -423948, -40605712] [2] 2064384 $$\Gamma_0(N)$$-optimal
141120.fs2 141120mh2 [0, 0, 0, 1551732, -311669008] [2] 4128768

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.fs

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{11} + 2q^{13} - 4q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.