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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 28224ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.bx3 | 28224ci1 | \([0, 0, 0, -1911, -31556]\) | \(140608/3\) | \(16467095232\) | \([2]\) | \(18432\) | \(0.74947\) | \(\Gamma_0(N)\)-optimal |
| 28224.bx2 | 28224ci2 | \([0, 0, 0, -4116, 54880]\) | \(21952/9\) | \(3161682284544\) | \([2, 2]\) | \(36864\) | \(1.0960\) | |
| 28224.bx4 | 28224ci3 | \([0, 0, 0, 13524, 400624]\) | \(97336/81\) | \(-227641124487168\) | \([2]\) | \(73728\) | \(1.4426\) | |
| 28224.bx1 | 28224ci4 | \([0, 0, 0, -57036, 5241040]\) | \(7301384/3\) | \(8431152758784\) | \([2]\) | \(73728\) | \(1.4426\) |
Rank
sage: E.rank()
The elliptic curves in class 28224ci have rank \(1\).
Complex multiplication
The elliptic curves in class 28224ci do not have complex multiplication.Modular form 28224.2.a.ci
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.
