# Properties

 Label 48400cd Number of curves 2 Conductor 48400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48400.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 48400cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.ba2 48400cd1 [0, -1, 0, 482992, -521703488] [] 1382400 $$\Gamma_0(N)$$-optimal
48400.ba1 48400cd2 [0, -1, 0, -287497008, -1876186263488] [] 6912000

## Rank

sage: E.rank()

The elliptic curves in class 48400cd have rank $$1$$.

## Modular form 48400.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{3} - 3q^{7} - 2q^{9} - 6q^{13} - 7q^{17} + 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 