# Properties

 Label 156090by Number of curves $2$ Conductor $156090$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("by1")

sage: E.isogeny_class()

## Elliptic curves in class 156090by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
156090.e2 156090by1 [1, 1, 0, -1240978, 551258932] [2] 6451200 $$\Gamma_0(N)$$-optimal
156090.e1 156090by2 [1, 1, 0, -20058898, 34570294708] [2] 12902400

## Rank

sage: E.rank()

The elliptic curves in class 156090by have rank $$1$$.

## Complex multiplication

The elliptic curves in class 156090by do not have complex multiplication.

## Modular form 156090.2.a.by

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.