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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 23520.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23520.bf1 | 23520bp4 | \([0, 1, 0, -23536, -1397656]\) | \(23937672968/45\) | \(2710632960\) | \([2]\) | \(36864\) | \(1.0653\) | |
23520.bf2 | 23520bp3 | \([0, 1, 0, -3936, 65484]\) | \(111980168/32805\) | \(1976051427840\) | \([2]\) | \(36864\) | \(1.0653\) | |
23520.bf3 | 23520bp1 | \([0, 1, 0, -1486, -21736]\) | \(48228544/2025\) | \(15247310400\) | \([2, 2]\) | \(18432\) | \(0.71870\) | \(\Gamma_0(N)\)-optimal |
23520.bf4 | 23520bp2 | \([0, 1, 0, 719, -78625]\) | \(85184/5625\) | \(-2710632960000\) | \([2]\) | \(36864\) | \(1.0653\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 23520.bf do not have complex multiplication.Modular form 23520.2.a.bf
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.