# Properties

 Label 53361bh Number of curves $2$ Conductor $53361$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 53361bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53361.bu2 53361bh1 [1, -1, 0, -13239, -583038] [] 51840 $$\Gamma_0(N)$$-optimal
53361.bu1 53361bh2 [1, -1, 0, -134514, 74263041] [] 570240

## Rank

sage: E.rank()

The elliptic curves in class 53361bh have rank $$0$$.

## Complex multiplication

The elliptic curves in class 53361bh do not have complex multiplication.

## Modular form 53361.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{5} - 3q^{8} + q^{10} + q^{13} - q^{16} + 5q^{17} + 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 