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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 14700f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14700.t2 | 14700f1 | \([0, -1, 0, -11433, 392862]\) | \(16384/3\) | \(30265205250000\) | \([2]\) | \(43008\) | \(1.3053\) | \(\Gamma_0(N)\)-optimal |
14700.t1 | 14700f2 | \([0, -1, 0, -54308, -4494888]\) | \(109744/9\) | \(1452729852000000\) | \([2]\) | \(86016\) | \(1.6519\) |
Rank
sage: E.rank()
The elliptic curves in class 14700f have rank \(1\).
Complex multiplication
The elliptic curves in class 14700f do not have complex multiplication.Modular form 14700.2.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 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.