# Properties

 Label 481338bv Number of curves $2$ Conductor $481338$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bv1")

sage: E.isogeny_class()

## Elliptic curves in class 481338bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
481338.bv1 481338bv1 $$[1, -1, 0, -42969240, 92853995328]$$ $$6793805286030262681/1048227429629952$$ $$1353752149594284531007488$$ $$$$ $$144506880$$ $$3.3538$$ $$\Gamma_0(N)$$-optimal
481338.bv2 481338bv2 $$[1, -1, 0, 74817000, 512290795968]$$ $$35862531227445945959/108547797844556928$$ $$-140186004021732513509039232$$ $$$$ $$289013760$$ $$3.7004$$

## Rank

sage: E.rank()

The elliptic curves in class 481338bv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 481338bv do not have complex multiplication.

## Modular form 481338.2.a.bv

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 4q^{5} + 2q^{7} - q^{8} - 4q^{10} + q^{13} - 2q^{14} + q^{16} - q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 