# Properties

 Label 430950hi Number of curves 2 Conductor 430950 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("430950.hi1")

sage: E.isogeny_class()

## Elliptic curves in class 430950hi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
430950.hi1 430950hi1 [1, 0, 0, -57544588, 166097243792]  61931520 $$\Gamma_0(N)$$-optimal
430950.hi2 430950hi2 [1, 0, 0, -8872588, 438125051792]  123863040

## Rank

sage: E.rank()

The elliptic curves in class 430950hi have rank $$0$$.

## Modular form 430950.2.a.hi

sage: E.q_eigenform(10)

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

## 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. 