# Properties

 Label 13200ce Number of curves 2 Conductor 13200 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("13200.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 13200ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13200.bu2 13200ce1 [0, 1, 0, 67, 138]  3072 $$\Gamma_0(N)$$-optimal
13200.bu1 13200ce2 [0, 1, 0, -308, 888]  6144

## Rank

sage: E.rank()

The elliptic curves in class 13200ce have rank $$1$$.

## Modular form 13200.2.a.bu

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} + q^{9} - q^{11} + 2q^{13} - 4q^{17} + 6q^{19} + O(q^{20})$$

## 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. 