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SageMath
E = EllipticCurve("jh1")
E.isogeny_class()
Elliptic curves in class 348480.jh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.jh1 | 348480jh4 | \([0, 0, 0, -2092332, -1164912496]\) | \(23937672968/45\) | \(1904347008368640\) | \([2]\) | \(5898240\) | \(2.1871\) | |
| 348480.jh2 | 348480jh3 | \([0, 0, 0, -349932, 55987184]\) | \(111980168/32805\) | \(1388268969100738560\) | \([2]\) | \(5898240\) | \(2.1871\) | |
| 348480.jh3 | 348480jh2 | \([0, 0, 0, -132132, -17803456]\) | \(48228544/2025\) | \(10711951922073600\) | \([2, 2]\) | \(2949120\) | \(1.8406\) | |
| 348480.jh4 | 348480jh1 | \([0, 0, 0, 3993, -1032856]\) | \(85184/5625\) | \(-464928468840000\) | \([2]\) | \(1474560\) | \(1.4940\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348480.jh have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.jh do not have complex multiplication.Modular form 348480.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
