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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 317900i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317900.i1 | 317900i1 | \([0, 1, 0, -44313, 3576268]\) | \(-996720640/187\) | \(-1805490161200\) | \([]\) | \(622080\) | \(1.3536\) | \(\Gamma_0(N)\)-optimal |
317900.i2 | 317900i2 | \([0, 1, 0, 13487, 12078648]\) | \(28098560/6539203\) | \(-63136185447002800\) | \([]\) | \(1866240\) | \(1.9029\) |
Rank
sage: E.rank()
The elliptic curves in class 317900i have rank \(1\).
Complex multiplication
The elliptic curves in class 317900i do not have complex multiplication.Modular form 317900.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.