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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 201810.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 201810.x1 | 201810cc3 | \([1, 0, 1, -3837774, 2893074616]\) | \(7043549569215769/1116465000\) | \(990866797207665000\) | \([2]\) | \(8847360\) | \(2.4635\) | |
| 201810.x2 | 201810cc4 | \([1, 0, 1, -1608254, -757249288]\) | \(518342813451289/20945456280\) | \(18589169548724566680\) | \([2]\) | \(8847360\) | \(2.4635\) | |
| 201810.x3 | 201810cc2 | \([1, 0, 1, -262854, 35998552]\) | \(2263054145689/678081600\) | \(601799916018369600\) | \([2, 2]\) | \(4423680\) | \(2.1169\) | |
| 201810.x4 | 201810cc1 | \([1, 0, 1, 44666, 3770456]\) | \(11104492391/13332480\) | \(-11832625076858880\) | \([2]\) | \(2211840\) | \(1.7703\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 201810.x have rank \(1\).
Complex multiplication
The elliptic curves in class 201810.x do not have complex multiplication.Modular form 201810.2.a.x
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.
