# Properties

 Label 84150fz Number of curves 2 Conductor 84150 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("84150.gl1")

sage: E.isogeny_class()

## Elliptic curves in class 84150fz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84150.gl2 84150fz1 [1, -1, 1, -198005, -14886003]  1032192 $$\Gamma_0(N)$$-optimal
84150.gl1 84150fz2 [1, -1, 1, -2646005, -1655046003]  2064384

## Rank

sage: E.rank()

The elliptic curves in class 84150fz have rank $$1$$.

## Modular form 84150.2.a.gl

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2q^{7} + q^{8} + q^{11} + 4q^{13} + 2q^{14} + q^{16} + q^{17} - 6q^{19} + O(q^{20})$$

## 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. 