Properties

 Label 58800hl Number of curves $2$ Conductor $58800$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hl1")

sage: E.isogeny_class()

Elliptic curves in class 58800hl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.n2 58800hl1 $$[0, -1, 0, 327, -5508]$$ $$16384/63$$ $$-14823774000$$ $$[2]$$ $$36864$$ $$0.63440$$ $$\Gamma_0(N)$$-optimal
58800.n1 58800hl2 $$[0, -1, 0, -3348, -64308]$$ $$1102736/147$$ $$553420896000$$ $$[2]$$ $$73728$$ $$0.98097$$

Rank

sage: E.rank()

The elliptic curves in class 58800hl have rank $$0$$.

Complex multiplication

The elliptic curves in class 58800hl do not have complex multiplication.

Modular form 58800.2.a.hl

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} - 2q^{13} - 2q^{17} - 2q^{19} + O(q^{20})$$

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.