# Properties

 Label 26b Number of curves $2$ Conductor $26$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

## Elliptic curves in class 26b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26.b2 26b1 $$[1, -1, 1, -3, 3]$$ $$-2146689/1664$$ $$-1664$$ $$$$ $$2$$ $$-0.68316$$ $$\Gamma_0(N)$$-optimal
26.b1 26b2 $$[1, -1, 1, -213, -1257]$$ $$-1064019559329/125497034$$ $$-125497034$$ $$[]$$ $$14$$ $$0.28979$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form26.2.a.b

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 