# Properties

 Label 150075.bj Number of curves 2 Conductor 150075 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("150075.bj1")
sage: E.isogeny_class()

## Elliptic curves in class 150075.bj

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
150075.bj1 150075bj1 [1, -1, 0, -84042, -9356009] 2 331776 $$\Gamma_0(N)$$-optimal
150075.bj2 150075bj2 [1, -1, 0, -78417, -10666634] 2 663552

## Rank

sage: E.rank()

The elliptic curves in class 150075.bj have rank $$2$$.

## Modular form 150075.2.a.bj

sage: E.q_eigenform(10)
$$q + q^{2} - q^{4} - 3q^{8} - 2q^{11} - 2q^{13} - q^{16} - 4q^{17} + O(q^{20})$$

## 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. 