Properties

 Label 10890.ba Number of curves 8 Conductor 10890 CM no Rank 0 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("10890.ba1")

sage: E.isogeny_class()

Elliptic curves in class 10890.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10890.ba1 10890ba7 [1, -1, 0, -5808204, -5386341240] [2] 276480
10890.ba2 10890ba8 [1, -1, 0, -493884, -18059112] [2] 276480
10890.ba3 10890ba6 [1, -1, 0, -363204, -84000240] [2, 2] 138240
10890.ba4 10890ba5 [1, -1, 0, -314199, 67866255] [2] 92160
10890.ba5 10890ba4 [1, -1, 0, -74619, -6738957] [2] 92160
10890.ba6 10890ba2 [1, -1, 0, -20169, 1003833] [2, 2] 46080
10890.ba7 10890ba3 [1, -1, 0, -14724, -2246832] [2] 69120
10890.ba8 10890ba1 [1, -1, 0, 1611, 76005] [2] 23040 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 10890.ba have rank $$0$$.

Modular form 10890.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 4q^{7} - q^{8} - q^{10} - 2q^{13} - 4q^{14} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20})$$

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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.