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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 286650d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286650.d2 | 286650d1 | \([1, -1, 0, -3809367, -20409255959]\) | \(-36495256013/1053197964\) | \(-176423250033940710937500\) | \([2]\) | \(40550400\) | \(3.1411\) | \(\Gamma_0(N)\)-optimal |
286650.d1 | 286650d2 | \([1, -1, 0, -137763117, -619316472209]\) | \(1726143065560493/9662982966\) | \(1618665168521279074218750\) | \([2]\) | \(81100800\) | \(3.4876\) |
Rank
sage: E.rank()
The elliptic curves in class 286650d have rank \(0\).
Complex multiplication
The elliptic curves in class 286650d do not have complex multiplication.Modular form 286650.2.a.d
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.