# Properties

 Label 75150f Number of curves 2 Conductor 75150 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("75150.u1")

sage: E.isogeny_class()

## Elliptic curves in class 75150f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.u2 75150f1 [1, -1, 0, -667992, -209979584]  627200 $$\Gamma_0(N)$$-optimal
75150.u1 75150f2 [1, -1, 0, -10687992, -13446399584]  1254400

## Rank

sage: E.rank()

The elliptic curves in class 75150f have rank $$0$$.

## Modular form 75150.2.a.u

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2q^{7} - q^{8} - 2q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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. 