# Properties

 Label 100016m Number of curves 2 Conductor 100016 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100016.g1")
sage: E.isogeny_class()

## Elliptic curves in class 100016m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100016.g1 100016m1 [0, 0, 0, -5171, -142350] 2 80640 $$\Gamma_0(N)$$-optimal
100016.g2 100016m2 [0, 0, 0, -2131, -308334] 2 161280

## Rank

sage: E.rank()

The elliptic curves in class 100016m have rank $$1$$.

## Modular form None

sage: E.q_eigenform(10)
$$q - 2q^{5} - q^{7} - 3q^{9} + 2q^{11} - 6q^{13} + 2q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 