# Properties

 Label 156090.bi Number of curves $4$ Conductor $156090$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 156090.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
156090.bi1 156090k4 [1, 0, 0, -101461, -12362965] [2] 1105920
156090.bi2 156090k2 [1, 0, 0, -10711, 106085] [2, 2] 552960
156090.bi3 156090k1 [1, 0, 0, -8291, 289521] [2] 276480 $$\Gamma_0(N)$$-optimal
156090.bi4 156090k3 [1, 0, 0, 41319, 844911] [2] 1105920

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 156090.2.a.bi

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.