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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 283920hh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.hh4 | 283920hh1 | \([0, 1, 0, 7380, 2914380]\) | \(35969456/2985255\) | \(-3688769459531520\) | \([2]\) | \(1720320\) | \(1.6665\) | \(\Gamma_0(N)\)-optimal |
| 283920.hh3 | 283920hh2 | \([0, 1, 0, -266400, 50990148]\) | \(423026849956/16769025\) | \(82883461930214400\) | \([2, 2]\) | \(3440640\) | \(2.0131\) | |
| 283920.hh1 | 283920hh3 | \([0, 1, 0, -4221000, 3336471828]\) | \(841356017734178/1404585\) | \(13884750887454720\) | \([2]\) | \(6881280\) | \(2.3596\) | |
| 283920.hh2 | 283920hh4 | \([0, 1, 0, -692280, -153261900]\) | \(3711757787138/1124589375\) | \(11116908782703360000\) | \([2]\) | \(6881280\) | \(2.3596\) |
Rank
sage: E.rank()
The elliptic curves in class 283920hh have rank \(1\).
Complex multiplication
The elliptic curves in class 283920hh do not have complex multiplication.Modular form 283920.2.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 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.
