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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 7581.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7581.d1 | 7581b5 | \([1, 1, 0, -283031, 57838326]\) | \(53297461115137/147\) | \(6915744507\) | \([2]\) | \(27648\) | \(1.5464\) | |
| 7581.d2 | 7581b4 | \([1, 1, 0, -17696, 897435]\) | \(13027640977/21609\) | \(1016614442529\) | \([2, 2]\) | \(13824\) | \(1.1999\) | |
| 7581.d3 | 7581b3 | \([1, 1, 0, -14086, -645479]\) | \(6570725617/45927\) | \(2160676176687\) | \([2]\) | \(13824\) | \(1.1999\) | |
| 7581.d4 | 7581b6 | \([1, 1, 0, -12281, 1463844]\) | \(-4354703137/17294403\) | \(-813630425504043\) | \([2]\) | \(27648\) | \(1.5464\) | |
| 7581.d5 | 7581b2 | \([1, 1, 0, -1451, 3960]\) | \(7189057/3969\) | \(186725101689\) | \([2, 2]\) | \(6912\) | \(0.85328\) | |
| 7581.d6 | 7581b1 | \([1, 1, 0, 354, 711]\) | \(103823/63\) | \(-2963890503\) | \([2]\) | \(3456\) | \(0.50670\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7581.d have rank \(0\).
Complex multiplication
The elliptic curves in class 7581.d do not have complex multiplication.Modular form 7581.2.a.d
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.
