Properties

 Label 86640.q Number of curves $2$ Conductor $86640$ CM no Rank $0$ Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86640.q1")

sage: E.isogeny_class()

Elliptic curves in class 86640.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86640.q1 86640bn2 [0, -1, 0, -412496, -101820480] [2] 491520
86640.q2 86640bn1 [0, -1, 0, -23376, -1894464] [2] 245760 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Modular form 86640.2.a.q

sage: E.q_eigenform(10)

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

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.