# Properties

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

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 26a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26.a2 26a1 $$[1, 0, 1, -5, -8]$$ $$-10218313/17576$$ $$-17576$$ $$$$ $$2$$ $$-0.49492$$ $$\Gamma_0(N)$$-optimal
26.a1 26a2 $$[1, 0, 1, -460, -3830]$$ $$-10730978619193/6656$$ $$-6656$$ $$[]$$ $$6$$ $$0.054386$$
26.a3 26a3 $$[1, 0, 1, 0, 0]$$ $$12167/26$$ $$-26$$ $$$$ $$6$$ $$-1.0442$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 26a do not have complex multiplication.

## Modular form26.2.a.a

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 