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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 9537j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9537.m3 | 9537j1 | \([1, 0, 1, -1885, -31381]\) | \(30664297/297\) | \(7168857993\) | \([2]\) | \(7680\) | \(0.71083\) | \(\Gamma_0(N)\)-optimal |
| 9537.m2 | 9537j2 | \([1, 0, 1, -3330, 22951]\) | \(169112377/88209\) | \(2129150823921\) | \([2, 2]\) | \(15360\) | \(1.0574\) | |
| 9537.m1 | 9537j3 | \([1, 0, 1, -42345, 3347029]\) | \(347873904937/395307\) | \(9541749988683\) | \([2]\) | \(30720\) | \(1.4040\) | |
| 9537.m4 | 9537j4 | \([1, 0, 1, 12565, 181901]\) | \(9090072503/5845851\) | \(-141104631876219\) | \([2]\) | \(30720\) | \(1.4040\) |
Rank
sage: E.rank()
The elliptic curves in class 9537j have rank \(0\).
Complex multiplication
The elliptic curves in class 9537j do not have complex multiplication.Modular form 9537.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
