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SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 277440hi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277440.hi4 | 277440hi1 | \([0, 1, 0, 1060, -140850]\) | \(85184/5625\) | \(-8689524840000\) | \([2]\) | \(589824\) | \(1.1624\) | \(\Gamma_0(N)\)-optimal |
| 277440.hi3 | 277440hi2 | \([0, 1, 0, -35065, -2445625]\) | \(48228544/2025\) | \(200206652313600\) | \([2, 2]\) | \(1179648\) | \(1.5089\) | |
| 277440.hi2 | 277440hi3 | \([0, 1, 0, -92865, 7623135]\) | \(111980168/32805\) | \(25946782139842560\) | \([2]\) | \(2359296\) | \(1.8555\) | |
| 277440.hi1 | 277440hi4 | \([0, 1, 0, -555265, -159441985]\) | \(23937672968/45\) | \(35592293744640\) | \([2]\) | \(2359296\) | \(1.8555\) |
Rank
sage: E.rank()
The elliptic curves in class 277440hi have rank \(0\).
Complex multiplication
The elliptic curves in class 277440hi do not have complex multiplication.Modular form 277440.2.a.hi
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.
