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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 331056.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 331056.bd1 | 331056bd3 | \([0, 0, 0, -1525506411, 22933438193050]\) | \(74220219816682217473/16416\) | \(86838223581609984\) | \([2]\) | \(58982400\) | \(3.5428\) | |
| 331056.bd2 | 331056bd2 | \([0, 0, 0, -95344491, 358332285850]\) | \(18120364883707393/269485056\) | \(1425536278315709497344\) | \([2, 2]\) | \(29491200\) | \(3.1963\) | |
| 331056.bd3 | 331056bd4 | \([0, 0, 0, -92556651, 380270913946]\) | \(-16576888679672833/2216253521952\) | \(-11723654900877092272078848\) | \([2]\) | \(58982400\) | \(3.5428\) | |
| 331056.bd4 | 331056bd1 | \([0, 0, 0, -6133611, 5253464986]\) | \(4824238966273/537919488\) | \(2845514910322195955712\) | \([2]\) | \(14745600\) | \(2.8497\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 331056.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 331056.bd do not have complex multiplication.Modular form 331056.2.a.bd
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.
