# Properties

 Label 102550.l Number of curves 2 Conductor 102550 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("102550.l1")

sage: E.isogeny_class()

## Elliptic curves in class 102550.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.l1 102550p2 [1, -1, 0, -191177, 32221581] [2] 394240
102550.l2 102550p1 [1, -1, 0, -11977, 503181] [2] 197120 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 102550.2.a.l

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.