# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("100016.a1")

sage: E.isogeny_class()

## Elliptic curves in class 100016.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100016.a1 100016a1 [0, 1, 0, -84, -164]  19712 $$\Gamma_0(N)$$-optimal
100016.a2 100016a2 [0, 1, 0, 296, -924]  39424

## Rank

sage: E.rank()

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

## Modular form 100016.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{5} - q^{7} + q^{9} + 2q^{13} + 4q^{15} + 6q^{17} - q^{19} + O(q^{20})$$

## 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 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. 