# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("100010.c1")
sage: E.isogeny_class()

## Elliptic curves in class 100010.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100010.c1 100010c1 [1, 1, 0, -5203, -146643] 2 102400 $$\Gamma_0(N)$$-optimal
100010.c2 100010c2 [1, 1, 0, -5123, -151267] 2 204800

## Rank

sage: E.rank()

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

## Modular form None

sage: E.q_eigenform(10)
$$q - q^{2} + 2q^{3} + q^{4} - q^{5} - 2q^{6} - 2q^{7} - q^{8} + q^{9} + q^{10} - 2q^{11} + 2q^{12} - 2q^{13} + 2q^{14} - 2q^{15} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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. 