Properties

 Label 23826y Number of curves 4 Conductor 23826 CM no Rank 1 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("23826.z1")

sage: E.isogeny_class()

Elliptic curves in class 23826y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23826.z3 23826y1 [1, 1, 1, -1993, -33133] [2] 27648 $$\Gamma_0(N)$$-optimal
23826.z4 23826y2 [1, 1, 1, 1617, -135657] [2] 55296
23826.z1 23826y3 [1, 1, 1, -29068, 1888109] [2] 82944
23826.z2 23826y4 [1, 1, 1, -14628, 3782637] [2] 165888

Rank

sage: E.rank()

The elliptic curves in class 23826y have rank $$1$$.

Modular form 23826.2.a.z

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + 2q^{7} + q^{8} + q^{9} - q^{11} - q^{12} + 4q^{13} + 2q^{14} + q^{16} - 6q^{17} + q^{18} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.