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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 346560.hh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.hh1 | 346560hh3 | \([0, 1, 0, -3523841, 2544808959]\) | \(784767874322/35625\) | \(219677918576640000\) | \([2]\) | \(8847360\) | \(2.4037\) | |
| 346560.hh2 | 346560hh4 | \([0, 1, 0, -1097921, -410446785]\) | \(23735908082/1954815\) | \(12054166748137390080\) | \([2]\) | \(8847360\) | \(2.4037\) | |
| 346560.hh3 | 346560hh2 | \([0, 1, 0, -231521, 35402655]\) | \(445138564/81225\) | \(250432827177369600\) | \([2, 2]\) | \(4423680\) | \(2.0572\) | |
| 346560.hh4 | 346560hh1 | \([0, 1, 0, 28399, 3224559]\) | \(3286064/7695\) | \(-5931303801569280\) | \([2]\) | \(2211840\) | \(1.7106\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.hh have rank \(0\).
Complex multiplication
The elliptic curves in class 346560.hh do not have complex multiplication.Modular form 346560.2.a.hh
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.
