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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 141570x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141570.fb3 | 141570x1 | \([1, -1, 1, -71897, -5347911]\) | \(31824875809/8785920\) | \(11346734258196480\) | \([2]\) | \(1105920\) | \(1.7881\) | \(\Gamma_0(N)\)-optimal |
| 141570.fb2 | 141570x2 | \([1, -1, 1, -420377, 100729401]\) | \(6361447449889/294465600\) | \(380292890372366400\) | \([2, 2]\) | \(2211840\) | \(2.1347\) | |
| 141570.fb1 | 141570x3 | \([1, -1, 1, -6649457, 6601397289]\) | \(25176685646263969/57915000\) | \(74795367424635000\) | \([2]\) | \(4423680\) | \(2.4813\) | |
| 141570.fb4 | 141570x4 | \([1, -1, 1, 233023, 384827721]\) | \(1083523132511/50179392120\) | \(-64805077626871004280\) | \([2]\) | \(4423680\) | \(2.4813\) |
Rank
sage: E.rank()
The elliptic curves in class 141570x have rank \(0\).
Complex multiplication
The elliptic curves in class 141570x do not have complex multiplication.Modular form 141570.2.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 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.
