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SageMath
sage: E = EllipticCurve("i1")
sage: E.isogeny_class()
Elliptic curves in class 23520.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.i1 | 23520bb4 | \([0, -1, 0, -23536, 1397656]\) | \(23937672968/45\) | \(2710632960\) | \([2]\) | \(36864\) | \(1.0653\) | |
| 23520.i2 | 23520bb3 | \([0, -1, 0, -3936, -65484]\) | \(111980168/32805\) | \(1976051427840\) | \([2]\) | \(36864\) | \(1.0653\) | |
| 23520.i3 | 23520bb1 | \([0, -1, 0, -1486, 21736]\) | \(48228544/2025\) | \(15247310400\) | \([2, 2]\) | \(18432\) | \(0.71870\) | \(\Gamma_0(N)\)-optimal |
| 23520.i4 | 23520bb2 | \([0, -1, 0, 719, 78625]\) | \(85184/5625\) | \(-2710632960000\) | \([2]\) | \(36864\) | \(1.0653\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.i have rank \(1\).
Complex multiplication
The elliptic curves in class 23520.i do not have complex multiplication.Modular form 23520.2.a.i
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.
