Properties

 Label 71058h Number of curves 2 Conductor 71058 CM no Rank 0 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("71058.h1")

sage: E.isogeny_class()

Elliptic curves in class 71058h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71058.h2 71058h1 [1, 1, 1, -397, -3709] [2] 71040 $$\Gamma_0(N)$$-optimal
71058.h1 71058h2 [1, 1, 1, -6637, -210877] [2] 142080

Rank

sage: E.rank()

The elliptic curves in class 71058h have rank $$0$$.

Modular form 71058.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + 4q^{7} + q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - q^{13} + 4q^{14} - 2q^{15} + q^{16} + q^{18} - 8q^{19} + O(q^{20})$$

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.