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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 9200.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9200.f1 | 9200bc2 | \([0, 1, 0, -46608, 3857428]\) | \(109348914285625/1472\) | \(150732800\) | \([]\) | \(10368\) | \(1.1262\) | |
9200.f2 | 9200bc1 | \([0, 1, 0, -608, 4468]\) | \(243135625/48668\) | \(4983603200\) | \([]\) | \(3456\) | \(0.57688\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9200.f have rank \(1\).
Complex multiplication
The elliptic curves in class 9200.f do not have complex multiplication.Modular form 9200.2.a.f
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 LMFDB 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 LMFDB labels.