Properties

 Label 73920ca Number of curves $6$ Conductor $73920$ CM no Rank $0$ Graph

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Show commands for: SageMath
sage: E = EllipticCurve("73920.eq1")

sage: E.isogeny_class()

Elliptic curves in class 73920ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.eq4 73920ca1 [0, 1, 0, -16961, 844575] [2] 131072 $$\Gamma_0(N)$$-optimal
73920.eq3 73920ca2 [0, 1, 0, -17281, 810719] [2, 2] 262144
73920.eq5 73920ca3 [0, 1, 0, 16319, 3612959] [2] 524288
73920.eq2 73920ca4 [0, 1, 0, -56001, -4153185] [2, 2] 524288
73920.eq6 73920ca5 [0, 1, 0, 116479, -24540321] [2] 1048576
73920.eq1 73920ca6 [0, 1, 0, -848001, -300836385] [2] 1048576

Rank

sage: E.rank()

The elliptic curves in class 73920ca have rank $$0$$.

Modular form 73920.2.a.eq

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} - q^{11} + 2q^{13} - q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.