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SageMath
E = EllipticCurve("nh1")
E.isogeny_class()
Elliptic curves in class 463680nh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.nh2 | 463680nh1 | \([0, 0, 0, -3166572, 2154891184]\) | \(18374873741826841/136564270080\) | \(26097838427555758080\) | \([2]\) | \(9830400\) | \(2.5562\) | \(\Gamma_0(N)\)-optimal |
463680.nh1 | 463680nh2 | \([0, 0, 0, -5286252, -1091610704]\) | \(85486955243540761/46777901234400\) | \(8939396136927913574400\) | \([2]\) | \(19660800\) | \(2.9028\) |
Rank
sage: E.rank()
The elliptic curves in class 463680nh have rank \(1\).
Complex multiplication
The elliptic curves in class 463680nh do not have complex multiplication.Modular form 463680.2.a.nh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.