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SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 87120.es
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.es1 | 87120fl4 | \([0, 0, 0, -72545187, -181876243934]\) | \(7981893677157049/1917731420550\) | \(10144516926608152014643200\) | \([2]\) | \(14745600\) | \(3.5094\) | |
| 87120.es2 | 87120fl2 | \([0, 0, 0, -24629187, 44661020866]\) | \(312341975961049/17862322500\) | \(94489056709419018240000\) | \([2, 2]\) | \(7372800\) | \(3.1628\) | |
| 87120.es3 | 87120fl1 | \([0, 0, 0, -24280707, 46050968194]\) | \(299270638153369/1069200\) | \(5655910614854860800\) | \([2]\) | \(3686400\) | \(2.8162\) | \(\Gamma_0(N)\)-optimal |
| 87120.es4 | 87120fl3 | \([0, 0, 0, 17711133, 182241656674]\) | \(116149984977671/2779502343750\) | \(-14703158258538710400000000\) | \([2]\) | \(14745600\) | \(3.5094\) |
Rank
sage: E.rank()
The elliptic curves in class 87120.es have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.es do not have complex multiplication.Modular form 87120.2.a.es
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.
