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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 372810.bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372810.bt1 | 372810bt2 | \([1, 0, 1, -99582839273, 12094989687470828]\) | \(920951868692595924370239353/46802812500000000000\) | \(5550246148462247812500000000000\) | \([2]\) | \(1544159232\) | \(4.9694\) | |
372810.bt2 | 372810bt1 | \([1, 0, 1, -6561276393, 167355600120556]\) | \(263419801326311610134393/50412272025600000000\) | \(5978284288905020822323200000000\) | \([2]\) | \(772079616\) | \(4.6228\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 372810.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 372810.bt do not have complex multiplication.Modular form 372810.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.