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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 66240.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66240.bs1 | 66240bq4 | \([0, 0, 0, -77766348, 263958505328]\) | \(544328872410114151778/14166950625\) | \(1353673212641280000\) | \([2]\) | \(3145728\) | \(2.9944\) | |
| 66240.bs2 | 66240bq3 | \([0, 0, 0, -7549068, -926549008]\) | \(497927680189263938/284271240234375\) | \(27162540000000000000000\) | \([2]\) | \(3145728\) | \(2.9944\) | |
| 66240.bs3 | 66240bq2 | \([0, 0, 0, -4866348, 4113745328]\) | \(266763091319403556/1355769140625\) | \(64772879385600000000\) | \([2, 2]\) | \(1572864\) | \(2.6479\) | |
| 66240.bs4 | 66240bq1 | \([0, 0, 0, -142428, 132425552]\) | \(-26752376766544/618796614375\) | \(-7390867159111680000\) | \([2]\) | \(786432\) | \(2.3013\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66240.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 66240.bs do not have complex multiplication.Modular form 66240.2.a.bs
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.
