# Properties

 Label 4026.e Number of curves 2 Conductor 4026 CM no Rank 0 Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("4026.e1")
sage: E.isogeny_class()

## Elliptic curves in class 4026.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4026.e1 4026b2 [1, 0, 1, -202144, 32870414] 2 116640
4026.e2 4026b1 [1, 0, 1, 10816, 2204174] 2 58320 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4026.e have rank $$0$$.

## Modular form4026.2.a.e

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 