Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2541.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2541.j1 | 2541l5 | \([1, 0, 1, -94867, 11238599]\) | \(53297461115137/147\) | \(260419467\) | \([2]\) | \(5120\) | \(1.2732\) | |
| 2541.j2 | 2541l4 | \([1, 0, 1, -5932, 175085]\) | \(13027640977/21609\) | \(38281661649\) | \([2, 2]\) | \(2560\) | \(0.92658\) | |
| 2541.j3 | 2541l3 | \([1, 0, 1, -4722, -124511]\) | \(6570725617/45927\) | \(81362482047\) | \([2]\) | \(2560\) | \(0.92658\) | |
| 2541.j4 | 2541l6 | \([1, 0, 1, -4117, 284711]\) | \(-4354703137/17294403\) | \(-30638089873083\) | \([2]\) | \(5120\) | \(1.2732\) | |
| 2541.j5 | 2541l2 | \([1, 0, 1, -487, 845]\) | \(7189057/3969\) | \(7031325609\) | \([2, 2]\) | \(1280\) | \(0.58001\) | |
| 2541.j6 | 2541l1 | \([1, 0, 1, 118, 119]\) | \(103823/63\) | \(-111608343\) | \([2]\) | \(640\) | \(0.23343\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2541.j have rank \(0\).
Complex multiplication
The elliptic curves in class 2541.j do not have complex multiplication.Modular form 2541.2.a.j
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.
