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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 32490z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.ba4 | 32490z1 | \([1, -1, 0, 11944881, -95369996435]\) | \(5495662324535111/117739817533440\) | \(-4038057441142510253506560\) | \([2]\) | \(6451200\) | \(3.4018\) | \(\Gamma_0(N)\)-optimal |
| 32490.ba3 | 32490z2 | \([1, -1, 0, -254213199, -1477635369107]\) | \(52974743974734147769/3152005008998400\) | \(108102573519697395925401600\) | \([2, 2]\) | \(12902400\) | \(3.7484\) | |
| 32490.ba2 | 32490z3 | \([1, -1, 0, -759497679, 6220575797485]\) | \(1412712966892699019449/330160465517040000\) | \(11323330989310445870622960000\) | \([2]\) | \(25804800\) | \(4.0949\) | |
| 32490.ba1 | 32490z4 | \([1, -1, 0, -4007457999, -97644024283667]\) | \(207530301091125281552569/805586668007040\) | \(27628760663801123320632960\) | \([2]\) | \(25804800\) | \(4.0949\) |
Rank
sage: E.rank()
The elliptic curves in class 32490z have rank \(0\).
Complex multiplication
The elliptic curves in class 32490z do not have complex multiplication.Modular form 32490.2.a.z
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.
