Properties

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

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

Elliptic curves in class 58800bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.l1 58800bg1 $$[0, -1, 0, -1147883, -472980738]$$ $$1950665639360512/492075$$ $$42195431250000$$ $$[2]$$ $$552960$$ $$1.9894$$ $$\Gamma_0(N)$$-optimal
58800.l2 58800bg2 $$[0, -1, 0, -1143508, -476769488]$$ $$-120527903507632/1937102445$$ $$-2657704554540000000$$ $$[2]$$ $$1105920$$ $$2.3360$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 58800.2.a.bg

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} - 2q^{13} - 6q^{17} - 2q^{19} + O(q^{20})$$

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.