# Properties

 Label 54978bv Number of curves $2$ Conductor $54978$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 54978bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54978.bi1 54978bv1 [1, 1, 1, -9605, 358091] [2] 138240 $$\Gamma_0(N)$$-optimal
54978.bi2 54978bv2 [1, 1, 1, -7645, 510971] [2] 276480

## Rank

sage: E.rank()

The elliptic curves in class 54978bv have rank $$1$$.

## Complex multiplication

The elliptic curves in class 54978bv do not have complex multiplication.

## Modular form 54978.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - 4q^{5} - q^{6} + q^{8} + q^{9} - 4q^{10} + q^{11} - q^{12} + 4q^{15} + q^{16} + q^{17} + q^{18} + O(q^{20})$$

## 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.