# Properties

 Label 100010.f Number of curves 2 Conductor 100010 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100010.f1")
sage: E.isogeny_class()

## Elliptic curves in class 100010.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100010.f1 100010e1 [1, -1, 1, -17216328052, -869056815249449] 2 222813696 $$\Gamma_0(N)$$-optimal
100010.f2 100010e2 [1, -1, 1, -14154486132, -1187958673848361] 2 445627392

## Rank

sage: E.rank()

The elliptic curves in class 100010.f have rank $$1$$.

## Modular form None

sage: E.q_eigenform(10)
$$q + q^{2} + q^{4} + q^{5} + q^{8} - 3q^{9} + q^{10} + 4q^{11} + 6q^{13} + q^{16} - 2q^{17} - 3q^{18} + 4q^{19} + O(q^{20})$$

## 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. 