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SageMath
E = EllipticCurve("jh1")
E.isogeny_class()
Elliptic curves in class 58800.jh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.jh1 | 58800iu4 | \([0, 1, 0, -7321008, 7621931988]\) | \(5763259856089/5670\) | \(42692469120000000\) | \([4]\) | \(1769472\) | \(2.4844\) | |
| 58800.jh2 | 58800iu2 | \([0, 1, 0, -461008, 117091988]\) | \(1439069689/44100\) | \(332052537600000000\) | \([2, 2]\) | \(884736\) | \(2.1378\) | |
| 58800.jh3 | 58800iu1 | \([0, 1, 0, -69008, -4428012]\) | \(4826809/1680\) | \(12649620480000000\) | \([2]\) | \(442368\) | \(1.7913\) | \(\Gamma_0(N)\)-optimal |
| 58800.jh4 | 58800iu3 | \([0, 1, 0, 126992, 395803988]\) | \(30080231/9003750\) | \(-67794059760000000000\) | \([2]\) | \(1769472\) | \(2.4844\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.jh have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.jh do not have complex multiplication.Modular form 58800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
