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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 31850cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31850.bq4 | 31850cb1 | \([1, 0, 0, -286063, -58835883]\) | \(1408317602329/2153060\) | \(3957896186562500\) | \([2]\) | \(331776\) | \(1.8925\) | \(\Gamma_0(N)\)-optimal |
| 31850.bq3 | 31850cb2 | \([1, 0, 0, -371813, -20677133]\) | \(3092354182009/1689383150\) | \(3105534972099218750\) | \([2]\) | \(663552\) | \(2.2391\) | |
| 31850.bq2 | 31850cb3 | \([1, 0, 0, -1161938, 424567492]\) | \(94376601570889/12235496000\) | \(22492091701625000000\) | \([2]\) | \(995328\) | \(2.4418\) | |
| 31850.bq1 | 31850cb4 | \([1, 0, 0, -17968938, 29315800492]\) | \(349046010201856969/7245875000\) | \(13319842935546875000\) | \([2]\) | \(1990656\) | \(2.7884\) |
Rank
sage: E.rank()
The elliptic curves in class 31850cb have rank \(0\).
Complex multiplication
The elliptic curves in class 31850cb do not have complex multiplication.Modular form 31850.2.a.cb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
