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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 3600o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3600.bo4 | 3600o1 | \([0, 0, 0, 825, -4250]\) | \(21296/15\) | \(-43740000000\) | \([2]\) | \(3072\) | \(0.73028\) | \(\Gamma_0(N)\)-optimal |
| 3600.bo3 | 3600o2 | \([0, 0, 0, -3675, -35750]\) | \(470596/225\) | \(2624400000000\) | \([2, 2]\) | \(6144\) | \(1.0769\) | |
| 3600.bo1 | 3600o3 | \([0, 0, 0, -48675, -4130750]\) | \(546718898/405\) | \(9447840000000\) | \([2]\) | \(12288\) | \(1.4234\) | |
| 3600.bo2 | 3600o4 | \([0, 0, 0, -30675, 2043250]\) | \(136835858/1875\) | \(43740000000000\) | \([2]\) | \(12288\) | \(1.4234\) |
Rank
sage: E.rank()
The elliptic curves in class 3600o have rank \(0\).
Complex multiplication
The elliptic curves in class 3600o do not have complex multiplication.Modular form 3600.2.a.o
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.
