# Properties

 Label 101478.k Number of curves 2 Conductor 101478 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("101478.k1")

sage: E.isogeny_class()

## Elliptic curves in class 101478.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
101478.k1 101478k2 [1, 0, 0, -3334962226, -74128716508108] [] 69895168
101478.k2 101478k1 [1, 0, 0, 8938334, 2268820292]  9985024 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 101478.k have rank $$0$$.

## Modular form 101478.2.a.k

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 