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SageMath
E = EllipticCurve("in1")
E.isogeny_class()
Elliptic curves in class 103488in
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
103488.ih3 | 103488in1 | \([0, 1, 0, -2417, -44913]\) | \(810448/33\) | \(63609520128\) | \([2]\) | \(98304\) | \(0.83879\) | \(\Gamma_0(N)\)-optimal |
103488.ih2 | 103488in2 | \([0, 1, 0, -6337, 133055]\) | \(3650692/1089\) | \(8396456656896\) | \([2, 2]\) | \(196608\) | \(1.1854\) | |
103488.ih4 | 103488in3 | \([0, 1, 0, 17183, 909215]\) | \(36382894/43923\) | \(-677314170322944\) | \([2]\) | \(393216\) | \(1.5319\) | |
103488.ih1 | 103488in4 | \([0, 1, 0, -92577, 10809567]\) | \(5690357426/891\) | \(13739656347648\) | \([2]\) | \(393216\) | \(1.5319\) |
Rank
sage: E.rank()
The elliptic curves in class 103488in have rank \(1\).
Complex multiplication
The elliptic curves in class 103488in do not have complex multiplication.Modular form 103488.2.a.in
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.