# Properties

 Label 106c Number of curves 2 Conductor 106 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("106.d1")

sage: E.isogeny_class()

## Elliptic curves in class 106c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106.d2 106c1 [1, 0, 0, -283, -2351]  48 $$\Gamma_0(N)$$-optimal
106.d1 106c2 [1, 0, 0, -24603, -1487407] [] 144

## Rank

sage: E.rank()

The elliptic curves in class 106c have rank $$0$$.

## Modular form106.2.a.d

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} - 2q^{9} + q^{12} + 5q^{13} - 4q^{14} + q^{16} - 3q^{17} - 2q^{18} - q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 