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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4830.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.n1 | 4830n3 | \([1, 0, 1, -841301318, -9392446043944]\) | \(65853432878493908038433301506521/38511703125000000\) | \(38511703125000000\) | \([2]\) | \(1290240\) | \(3.4077\) | |
4830.n2 | 4830n2 | \([1, 0, 1, -52581638, -146758467112]\) | \(16077778198622525072705635801/388799208512064000000\) | \(388799208512064000000\) | \([2, 2]\) | \(645120\) | \(3.0612\) | |
4830.n3 | 4830n4 | \([1, 0, 1, -50621638, -158203299112]\) | \(-14346048055032350809895395801/2509530875136386550792000\) | \(-2509530875136386550792000\) | \([4]\) | \(1290240\) | \(3.4077\) | |
4830.n4 | 4830n1 | \([1, 0, 1, -3409158, -2112699944]\) | \(4381924769947287308715481/608122186185572352000\) | \(608122186185572352000\) | \([2]\) | \(322560\) | \(2.7146\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4830.n have rank \(0\).
Complex multiplication
The elliptic curves in class 4830.n do not have complex multiplication.Modular form 4830.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.