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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 28322g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28322.k2 | 28322g1 | \([1, 1, 0, 445777, 22410725]\) | \(3449795831/2071552\) | \(-5882712279279066112\) | \([2]\) | \(1105920\) | \(2.2908\) | \(\Gamma_0(N)\)-optimal |
28322.k1 | 28322g2 | \([1, 1, 0, -1819983, 178748165]\) | \(234770924809/130960928\) | \(371897716905673460768\) | \([2]\) | \(2211840\) | \(2.6374\) |
Rank
sage: E.rank()
The elliptic curves in class 28322g have rank \(0\).
Complex multiplication
The elliptic curves in class 28322g do not have complex multiplication.Modular form 28322.2.a.g
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.