Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 305760.dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 305760.dj1 | 305760dj2 | \([0, -1, 0, -1255666225, 17126556305377]\) | \(454357982636417669333824/3003024375\) | \(1447128328988160000\) | \([2]\) | \(82575360\) | \(3.5437\) | |
| 305760.dj2 | 305760dj4 | \([0, -1, 0, -83863320, 228806497620]\) | \(1082883335268084577352/251301565117746585\) | \(15137473451283337205076480\) | \([2]\) | \(82575360\) | \(3.5437\) | |
| 305760.dj3 | 305760dj1 | \([0, -1, 0, -78480670, 267611098000]\) | \(7099759044484031233216/577161945398025\) | \(4345761645704463566400\) | \([2, 2]\) | \(41287680\) | \(3.1971\) | \(\Gamma_0(N)\)-optimal |
| 305760.dj4 | 305760dj3 | \([0, -1, 0, -73122520, 305713974280]\) | \(-717825640026599866952/254764560814329735\) | \(-15346071457405480444423680\) | \([2]\) | \(82575360\) | \(3.5437\) |
Rank
sage: E.rank()
The elliptic curves in class 305760.dj have rank \(1\).
Complex multiplication
The elliptic curves in class 305760.dj do not have complex multiplication.Modular form 305760.2.a.dj
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
