# Properties

 Label 48400.bd Number of curves 3 Conductor 48400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48400.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 48400.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.bd1 48400cz3 [0, -1, 0, -1467876208, 21646998590912] [] 17280000
48400.bd2 48400cz1 [0, -1, 0, -1356208, -608049088] [] 691200 $$\Gamma_0(N)$$-optimal
48400.bd3 48400cz2 [0, -1, 0, 9533792, 6376070912] [] 3456000

## Rank

sage: E.rank()

The elliptic curves in class 48400.bd have rank $$0$$.

## Modular form 48400.2.a.bd

sage: E.q_eigenform(10)

$$q - q^{3} - 3q^{7} - 2q^{9} + 4q^{13} + 3q^{17} - 5q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 