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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 483483q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
483483.q2 | 483483q1 | \([1, 0, 0, -406309, 99651824]\) | \(63052870949070913/3581721\) | \(421385893929\) | \([2]\) | \(2557440\) | \(1.6971\) | \(\Gamma_0(N)\)-optimal |
483483.q1 | 483483q2 | \([1, 0, 0, -407044, 99273005]\) | \(63395672188101553/475137974883\) | \(55899507607010067\) | \([2]\) | \(5114880\) | \(2.0437\) |
Rank
sage: E.rank()
The elliptic curves in class 483483q have rank \(1\).
Complex multiplication
The elliptic curves in class 483483q do not have complex multiplication.Modular form 483483.2.a.q
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.