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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2240.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2240.n1 | 2240f3 | \([0, 0, 0, -17132, -863056]\) | \(2121328796049/120050\) | \(31470387200\) | \([2]\) | \(3072\) | \(1.0787\) | |
2240.n2 | 2240f4 | \([0, 0, 0, -5612, 151216]\) | \(74565301329/5468750\) | \(1433600000000\) | \([4]\) | \(3072\) | \(1.0787\) | |
2240.n3 | 2240f2 | \([0, 0, 0, -1132, -11856]\) | \(611960049/122500\) | \(32112640000\) | \([2, 2]\) | \(1536\) | \(0.73213\) | |
2240.n4 | 2240f1 | \([0, 0, 0, 148, -1104]\) | \(1367631/2800\) | \(-734003200\) | \([2]\) | \(768\) | \(0.38556\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2240.n have rank \(0\).
Complex multiplication
The elliptic curves in class 2240.n do not have complex multiplication.Modular form 2240.2.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.