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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3920.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3920.t1 | 3920ba3 | \([0, 0, 0, -209867, -37003526]\) | \(2121328796049/120050\) | \(57850930995200\) | \([2]\) | \(18432\) | \(1.7051\) | |
| 3920.t2 | 3920ba4 | \([0, 0, 0, -68747, 6483386]\) | \(74565301329/5468750\) | \(2635337600000000\) | \([4]\) | \(18432\) | \(1.7051\) | |
| 3920.t3 | 3920ba2 | \([0, 0, 0, -13867, -508326]\) | \(611960049/122500\) | \(59031562240000\) | \([2, 2]\) | \(9216\) | \(1.3585\) | |
| 3920.t4 | 3920ba1 | \([0, 0, 0, 1813, -47334]\) | \(1367631/2800\) | \(-1349292851200\) | \([2]\) | \(4608\) | \(1.0119\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3920.t have rank \(0\).
Complex multiplication
The elliptic curves in class 3920.t do not have complex multiplication.Modular form 3920.2.a.t
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.
