# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("102550.q1")

sage: E.isogeny_class()

## Elliptic curves in class 102550g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.q2 102550g1 [1, -1, 0, 239708, 291889616] [] 9483264 $$\Gamma_0(N)$$-optimal
102550.q1 102550g2 [1, -1, 0, -138649042, -628720244134] [] 66382848

## Rank

sage: E.rank()

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

## Modular form 102550.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} + 3q^{3} + q^{4} - 3q^{6} - q^{7} - q^{8} + 6q^{9} + 5q^{11} + 3q^{12} - 7q^{13} + q^{14} + q^{16} + 3q^{17} - 6q^{18} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 