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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 128934.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 128934.bc1 | 128934bj4 | \([1, -1, 1, -144533506496, 21149575954099845]\) | \(458038307459437803276572539343003833/86000447460798\) | \(62694326198921742\) | \([2]\) | \(327352320\) | \(4.5168\) | |
| 128934.bc2 | 128934bj2 | \([1, -1, 1, -9033344186, 330463815752661]\) | \(111825759760338976846738658338393/1532291201797601099556\) | \(1117040286110451201576324\) | \([2, 2]\) | \(163676160\) | \(4.1702\) | |
| 128934.bc3 | 128934bj3 | \([1, -1, 1, -9025319156, 331080266457141]\) | \(-111527993597885114164012178708473/413980765601504764798430334\) | \(-301791978123496973538055713486\) | \([2]\) | \(327352320\) | \(4.5168\) | |
| 128934.bc4 | 128934bj1 | \([1, -1, 1, -565085606, 5153968750245]\) | \(27374041292637614212993237273/101051566314387812377488\) | \(73666591843188715223188752\) | \([2]\) | \(81838080\) | \(3.8236\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 128934.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 128934.bc do not have complex multiplication.Modular form 128934.2.a.bc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
