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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 67760.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67760.x1 | 67760c4 | \([0, 0, 0, -395171843, -3022165163358]\) | \(1881029584733429900898/1046747344575625\) | \(3797763630087657063680000\) | \([2]\) | \(11796480\) | \(3.6639\) | |
| 67760.x2 | 67760c3 | \([0, 0, 0, -230021363, 1322813016338]\) | \(370972884164057659458/6332855224609375\) | \(22976592557187500000000000\) | \([2]\) | \(11796480\) | \(3.6639\) | |
| 67760.x3 | 67760c2 | \([0, 0, 0, -29146843, -29032328358]\) | \(1509531602170901796/672851175390625\) | \(1220604826753219600000000\) | \([2, 2]\) | \(5898240\) | \(3.3173\) | |
| 67760.x4 | 67760c1 | \([0, 0, 0, 6284377, -3387211322]\) | \(60522147178827696/45953185114375\) | \(-20840670867048266080000\) | \([2]\) | \(2949120\) | \(2.9707\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67760.x have rank \(0\).
Complex multiplication
The elliptic curves in class 67760.x do not have complex multiplication.Modular form 67760.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
