Properties

 Label 273273br Number of curves 6 Conductor 273273 CM no Rank 0 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("273273.br1")

sage: E.isogeny_class()

Elliptic curves in class 273273br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
273273.br4 273273br1 [1, 0, 1, -281727, -57560891] [2] 1843200 $$\Gamma_0(N)$$-optimal
273273.br3 273273br2 [1, 0, 1, -323132, -39541435] [2, 2] 3686400
273273.br2 273273br3 [1, 0, 1, -2351977, 1360361615] [2, 2] 7372800
273273.br6 273273br4 [1, 0, 1, 1043233, -286033681] [2] 7372800
273273.br1 273273br5 [1, 0, 1, -37422012, 88109600191] [2] 14745600
273273.br5 273273br6 [1, 0, 1, 256538, 4213033619] [2] 14745600

Rank

sage: E.rank()

The elliptic curves in class 273273br have rank $$0$$.

Modular form 273273.2.a.br

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} - 3q^{8} + q^{9} - 2q^{10} + q^{11} - q^{12} - 2q^{15} - q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.