# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("48576.t1")

sage: E.isogeny_class()

## Elliptic curves in class 48576.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48576.t1 48576cm2 [0, -1, 0, -79233, 8544033]  163840
48576.t2 48576cm1 [0, -1, 0, -1473, 317025]  81920 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 48576.2.a.t

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 LMFDB 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 LMFDB labels. 