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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 1440.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1440.n1 | 1440n3 | \([0, 0, 0, -32412, 2245984]\) | \(1261112198464/675\) | \(2015539200\) | \([4]\) | \(3072\) | \(1.1149\) | |
| 1440.n2 | 1440n2 | \([0, 0, 0, -4467, -63974]\) | \(26410345352/10546875\) | \(3936600000000\) | \([2]\) | \(3072\) | \(1.1149\) | |
| 1440.n3 | 1440n1 | \([0, 0, 0, -2037, 34684]\) | \(20034997696/455625\) | \(21257640000\) | \([2, 2]\) | \(1536\) | \(0.76837\) | \(\Gamma_0(N)\)-optimal |
| 1440.n4 | 1440n4 | \([0, 0, 0, 213, 107134]\) | \(2863288/13286025\) | \(-4958982259200\) | \([2]\) | \(3072\) | \(1.1149\) |
Rank
sage: E.rank()
The elliptic curves in class 1440.n have rank \(0\).
Complex multiplication
The elliptic curves in class 1440.n do not have complex multiplication.Modular form 1440.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
