Properties

 Label 86640.d Number of curves $2$ Conductor $86640$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 86640.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86640.d1 86640bq2 $$[0, -1, 0, -21059416, -37190773520]$$ $$781484460931/900$$ $$1189555929092505600$$ $$$$ $$3502080$$ $$2.7524$$
86640.d2 86640bq1 $$[0, -1, 0, -1305496, -590710544]$$ $$-186169411/6480$$ $$-8564802689466040320$$ $$$$ $$1751040$$ $$2.4058$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 86640.d have rank $$0$$.

Complex multiplication

The elliptic curves in class 86640.d do not have complex multiplication.

Modular form 86640.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 2 q^{7} + q^{9} + 2 q^{13} + q^{15} - 6 q^{17} + O(q^{20})$$ 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 LMFDB 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 LMFDB labels. 