# Properties

 Label 26.a Number of curves 3 Conductor 26 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("26.a1")

sage: E.isogeny_class()

## Elliptic curves in class 26.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26.a1 26a2 [1, 0, 1, -460, -3830] [] 6
26.a2 26a1 [1, 0, 1, -5, -8]  2 $$\Gamma_0(N)$$-optimal
26.a3 26a3 [1, 0, 1, 0, 0]  6

## Rank

sage: E.rank()

The elliptic curves in class 26.a have rank $$0$$.

## Modular form26.2.a.a

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 