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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 92400.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.t1 | 92400ez4 | \([0, -1, 0, -106476448, -422843595008]\) | \(260744057755293612689909/8504954620259328\) | \(4354536765572775936000\) | \([2]\) | \(9216000\) | \(3.2462\) | |
| 92400.t2 | 92400ez3 | \([0, -1, 0, -6943648, -6000228608]\) | \(72313087342699809269/11447096545640448\) | \(5860913431367909376000\) | \([2]\) | \(4608000\) | \(2.8996\) | |
| 92400.t3 | 92400ez2 | \([0, -1, 0, -1884048, 986880192]\) | \(1444540994277943589/15251205665388\) | \(7808617300678656000\) | \([2]\) | \(1843200\) | \(2.4414\) | |
| 92400.t4 | 92400ez1 | \([0, -1, 0, -1879248, 992198592]\) | \(1433528304665250149/162339408\) | \(83117776896000\) | \([2]\) | \(921600\) | \(2.0949\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.t have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.t do not have complex multiplication.Modular form 92400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
