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SageMath
E = EllipticCurve("iq1")
E.isogeny_class()
Elliptic curves in class 100800.iq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.iq1 | 100800oa4 | \([0, 0, 0, -201900, 34918000]\) | \(2438569736/21\) | \(7838208000000\) | \([2]\) | \(524288\) | \(1.6420\) | |
100800.iq2 | 100800oa2 | \([0, 0, 0, -12900, 520000]\) | \(5088448/441\) | \(20575296000000\) | \([2, 2]\) | \(262144\) | \(1.2954\) | |
100800.iq3 | 100800oa1 | \([0, 0, 0, -2775, -47000]\) | \(3241792/567\) | \(413343000000\) | \([2]\) | \(131072\) | \(0.94882\) | \(\Gamma_0(N)\)-optimal |
100800.iq4 | 100800oa3 | \([0, 0, 0, 14100, 2410000]\) | \(830584/7203\) | \(-2688505344000000\) | \([2]\) | \(524288\) | \(1.6420\) |
Rank
sage: E.rank()
The elliptic curves in class 100800.iq have rank \(2\).
Complex multiplication
The elliptic curves in class 100800.iq do not have complex multiplication.Modular form 100800.2.a.iq
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 LMFDB 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 LMFDB labels.