# Properties

 Label 102550.bb Number of curves 2 Conductor 102550 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("102550.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 102550.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.bb1 102550s1 [1, 1, 1, -1621913, 794409031] [] 2643840 $$\Gamma_0(N)$$-optimal
102550.bb2 102550s2 [1, 1, 1, -120288, 2192385281] [] 7931520

## Rank

sage: E.rank()

The elliptic curves in class 102550.bb have rank $$0$$.

## Modular form 102550.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - q^{7} + q^{8} + q^{9} - 6q^{11} + 2q^{12} + q^{13} - q^{14} + q^{16} + 3q^{17} + q^{18} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 