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SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 430950hi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.hi1 | 430950hi1 | \([1, 0, 0, -57544588, 166097243792]\) | \(279419703685750081/3666124800000\) | \(276495065308800000000000\) | \([2]\) | \(61931520\) | \(3.3057\) | \(\Gamma_0(N)\)-optimal |
430950.hi2 | 430950hi2 | \([1, 0, 0, -8872588, 438125051792]\) | \(-1024222994222401/1098922500000000\) | \(-82879515832851562500000000\) | \([2]\) | \(123863040\) | \(3.6523\) |
Rank
sage: E.rank()
The elliptic curves in class 430950hi have rank \(0\).
Complex multiplication
The elliptic curves in class 430950hi do not have complex multiplication.Modular form 430950.2.a.hi
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.