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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 127296.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127296.n1 | 127296bv1 | \([0, 0, 0, -1018956, 141828464]\) | \(612241204436497/308834353152\) | \(59019163978382180352\) | \([2]\) | \(2752512\) | \(2.4863\) | \(\Gamma_0(N)\)-optimal |
127296.n2 | 127296bv2 | \([0, 0, 0, 3773364, 1094541680]\) | \(31091549545392623/20700995942016\) | \(-3956021930683181039616\) | \([2]\) | \(5505024\) | \(2.8329\) |
Rank
sage: E.rank()
The elliptic curves in class 127296.n have rank \(0\).
Complex multiplication
The elliptic curves in class 127296.n do not have complex multiplication.Modular form 127296.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.