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SageMath
E = EllipticCurve("hj1")
E.isogeny_class()
Elliptic curves in class 129360hj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.gn2 | 129360hj1 | \([0, 1, 0, 215, -442]\) | \(199344128/136125\) | \(-747054000\) | \([2]\) | \(46080\) | \(0.39127\) | \(\Gamma_0(N)\)-optimal |
129360.gn1 | 129360hj2 | \([0, 1, 0, -940, -4600]\) | \(1047213232/515625\) | \(45276000000\) | \([2]\) | \(92160\) | \(0.73785\) |
Rank
sage: E.rank()
The elliptic curves in class 129360hj have rank \(1\).
Complex multiplication
The elliptic curves in class 129360hj do not have complex multiplication.Modular form 129360.2.a.hj
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.