Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 100800.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.v1 | 100800me6 | \([0, 0, 0, -11289900, -14601022000]\) | \(53297461115137/147\) | \(438939648000000\) | \([2]\) | \(2097152\) | \(2.4680\) | |
| 100800.v2 | 100800me4 | \([0, 0, 0, -705900, -227950000]\) | \(13027640977/21609\) | \(64524128256000000\) | \([2, 2]\) | \(1048576\) | \(2.1214\) | |
| 100800.v3 | 100800me3 | \([0, 0, 0, -561900, 161138000]\) | \(6570725617/45927\) | \(137137287168000000\) | \([2]\) | \(1048576\) | \(2.1214\) | |
| 100800.v4 | 100800me5 | \([0, 0, 0, -489900, -370078000]\) | \(-4354703137/17294403\) | \(-51640810647552000000\) | \([2]\) | \(2097152\) | \(2.4680\) | |
| 100800.v5 | 100800me2 | \([0, 0, 0, -57900, -1150000]\) | \(7189057/3969\) | \(11851370496000000\) | \([2, 2]\) | \(524288\) | \(1.7748\) | |
| 100800.v6 | 100800me1 | \([0, 0, 0, 14100, -142000]\) | \(103823/63\) | \(-188116992000000\) | \([2]\) | \(262144\) | \(1.4282\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.v have rank \(1\).
Complex multiplication
The elliptic curves in class 100800.v do not have complex multiplication.Modular form 100800.2.a.v
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
