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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 312650.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 312650.be1 | 312650be1 | \([1, 1, 0, -226125, 41294375]\) | \(-16954786009/370\) | \(-27904989531250\) | \([]\) | \(1866240\) | \(1.6960\) | \(\Gamma_0(N)\)-optimal |
| 312650.be2 | 312650be2 | \([1, 1, 0, -78250, 94381500]\) | \(-702595369/50653000\) | \(-3820193066828125000\) | \([]\) | \(5598720\) | \(2.2453\) | |
| 312650.be3 | 312650be3 | \([1, 1, 0, 703375, -2531096875]\) | \(510273943271/37000000000\) | \(-2790498953125000000000\) | \([]\) | \(16796160\) | \(2.7946\) |
Rank
sage: E.rank()
The elliptic curves in class 312650.be have rank \(2\).
Complex multiplication
The elliptic curves in class 312650.be do not have complex multiplication.Modular form 312650.2.a.be
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
