# Properties

 Label 48576bd Number of curves 2 Conductor 48576 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48576.cu1")

sage: E.isogeny_class()

## Elliptic curves in class 48576bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48576.cu2 48576bd1 [0, 1, 0, -1473, -317025]  81920 $$\Gamma_0(N)$$-optimal
48576.cu1 48576bd2 [0, 1, 0, -79233, -8544033]  163840

## Rank

sage: E.rank()

The elliptic curves in class 48576bd have rank $$1$$.

## Modular form 48576.2.a.cu

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} + q^{9} - q^{11} - 2q^{13} - 2q^{19} + O(q^{20})$$

## 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 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. 