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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 124950.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 124950.ce1 | 124950bc6 | \([1, 1, 0, -2134660525, 37960386875125]\) | \(585196747116290735872321/836876053125000\) | \(1538400480845361328125000\) | \([2]\) | \(84934656\) | \(3.9123\) | |
| 124950.ce2 | 124950bc4 | \([1, 1, 0, -309459525, -2095132789875]\) | \(1782900110862842086081/328139630024640\) | \(603207802074513615000000\) | \([2]\) | \(42467328\) | \(3.5658\) | |
| 124950.ce3 | 124950bc3 | \([1, 1, 0, -134627525, 581770138125]\) | \(146796951366228945601/5397929064360000\) | \(9922827445201400625000000\) | \([2, 2]\) | \(42467328\) | \(3.5658\) | |
| 124950.ce4 | 124950bc2 | \([1, 1, 0, -21339525, -25566829875]\) | \(584614687782041281/184812061593600\) | \(339733659912897600000000\) | \([2, 2]\) | \(21233664\) | \(3.2192\) | |
| 124950.ce5 | 124950bc1 | \([1, 1, 0, 3748475, -2711661875]\) | \(3168685387909439/3563732336640\) | \(-6551086651146240000000\) | \([2]\) | \(10616832\) | \(2.8726\) | \(\Gamma_0(N)\)-optimal |
| 124950.ce6 | 124950bc5 | \([1, 1, 0, 52797475, 2074985113125]\) | \(8854313460877886399/1016927675429790600\) | \(-1869383188853741160928125000\) | \([2]\) | \(84934656\) | \(3.9123\) |
Rank
sage: E.rank()
The elliptic curves in class 124950.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 124950.ce do not have complex multiplication.Modular form 124950.2.a.ce
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
