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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 425880n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.n4 | 425880n1 | \([0, 0, 0, 33462, 1364337]\) | \(73598976/56875\) | \(-3202056822510000\) | \([2]\) | \(2064384\) | \(1.6633\) | \(\Gamma_0(N)\)-optimal* |
425880.n3 | 425880n2 | \([0, 0, 0, -156663, 11745162]\) | \(472058064/207025\) | \(186487789342982400\) | \([2, 2]\) | \(4128768\) | \(2.0098\) | \(\Gamma_0(N)\)-optimal* |
425880.n1 | 425880n3 | \([0, 0, 0, -2133963, 1199311542]\) | \(298261205316/156065\) | \(562332410941916160\) | \([2]\) | \(8257536\) | \(2.3564\) | \(\Gamma_0(N)\)-optimal* |
425880.n2 | 425880n4 | \([0, 0, 0, -1221363, -511448418]\) | \(55920415716/999635\) | \(3601878445595888640\) | \([2]\) | \(8257536\) | \(2.3564\) |
Rank
sage: E.rank()
The elliptic curves in class 425880n have rank \(0\).
Complex multiplication
The elliptic curves in class 425880n do not have complex multiplication.Modular form 425880.2.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 Cremona 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 Cremona labels.