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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2480.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2480.n1 | 2480i4 | \([0, -1, 0, -32736, -984064]\) | \(947226559343329/443751840500\) | \(1817607538688000\) | \([2]\) | \(13824\) | \(1.6224\) | |
| 2480.n2 | 2480i2 | \([0, -1, 0, -27296, -1726720]\) | \(549131937598369/307520\) | \(1259601920\) | \([2]\) | \(4608\) | \(1.0731\) | |
| 2480.n3 | 2480i1 | \([0, -1, 0, -1696, -26880]\) | \(-131794519969/3174400\) | \(-13002342400\) | \([2]\) | \(2304\) | \(0.72649\) | \(\Gamma_0(N)\)-optimal |
| 2480.n4 | 2480i3 | \([0, -1, 0, 7264, -120064]\) | \(10347405816671/7447750000\) | \(-30505984000000\) | \([2]\) | \(6912\) | \(1.2758\) |
Rank
sage: E.rank()
The elliptic curves in class 2480.n have rank \(0\).
Complex multiplication
The elliptic curves in class 2480.n do not have complex multiplication.Modular form 2480.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
