# Properties

 Label 26011a Number of curves $3$ Conductor $26011$ CM no Rank $1$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 26011a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26011.a3 26011a1 $$[0, 1, 1, 913, -165]$$ $$32768/19$$ $$-48748801771$$ $$[]$$ $$17280$$ $$0.74029$$ $$\Gamma_0(N)$$-optimal
26011.a2 26011a2 $$[0, 1, 1, -12777, -595680]$$ $$-89915392/6859$$ $$-17598317439331$$ $$[]$$ $$51840$$ $$1.2896$$
26011.a1 26011a3 $$[0, 1, 1, -1053217, -416381515]$$ $$-50357871050752/19$$ $$-48748801771$$ $$[]$$ $$155520$$ $$1.8389$$

## Rank

sage: E.rank()

The elliptic curves in class 26011a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 26011a do not have complex multiplication.

## Modular form 26011.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{4} - 3q^{5} - q^{7} + q^{9} + 3q^{11} + 4q^{12} + 4q^{13} + 6q^{15} + 4q^{16} + 3q^{17} - q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 