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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4598.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4598.f1 | 4598d1 | \([1, -1, 0, -446, -3008]\) | \(5545233/836\) | \(1481024996\) | \([2]\) | \(2400\) | \(0.48376\) | \(\Gamma_0(N)\)-optimal |
4598.f2 | 4598d2 | \([1, -1, 0, 764, -17286]\) | \(27818127/87362\) | \(-154767112082\) | \([2]\) | \(4800\) | \(0.83034\) |
Rank
sage: E.rank()
The elliptic curves in class 4598.f have rank \(0\).
Complex multiplication
The elliptic curves in class 4598.f do not have complex multiplication.Modular form 4598.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.