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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1288i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1288.g2 | 1288i1 | \([0, -1, 0, -2632, 52860]\) | \(1969910093092/7889\) | \(8078336\) | \([2]\) | \(480\) | \(0.53679\) | \(\Gamma_0(N)\)-optimal |
1288.g1 | 1288i2 | \([0, -1, 0, -2672, 51212]\) | \(1030541881826/62236321\) | \(127459985408\) | \([2]\) | \(960\) | \(0.88336\) |
Rank
sage: E.rank()
The elliptic curves in class 1288i have rank \(0\).
Complex multiplication
The elliptic curves in class 1288i do not have complex multiplication.Modular form 1288.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.