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SageMath
E = EllipticCurve("jh1")
E.isogeny_class()
Elliptic curves in class 202800.jh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.jh1 | 202800ba4 | \([0, 1, 0, -55974208, -160680894412]\) | \(502270291349/1889568\) | \(72964670628096000000000\) | \([2]\) | \(18432000\) | \(3.2464\) | |
| 202800.jh2 | 202800ba2 | \([0, 1, 0, -3584208, 2610285588]\) | \(131872229/18\) | \(695060496000000000\) | \([2]\) | \(3686400\) | \(2.4416\) | |
| 202800.jh3 | 202800ba3 | \([0, 1, 0, -1894208, -4822334412]\) | \(-19465109/248832\) | \(-9608516296704000000000\) | \([2]\) | \(9216000\) | \(2.8998\) | |
| 202800.jh4 | 202800ba1 | \([0, 1, 0, -204208, 48245588]\) | \(-24389/12\) | \(-463373664000000000\) | \([2]\) | \(1843200\) | \(2.0951\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.jh have rank \(0\).
Complex multiplication
The elliptic curves in class 202800.jh do not have complex multiplication.Modular form 202800.2.a.jh
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
