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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 102960.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.bp1 | 102960de2 | \([0, 0, 0, -2398683, -1429926262]\) | \(-511157582445795481/8504770560\) | \(-25395108815831040\) | \([]\) | \(1244160\) | \(2.2787\) | |
102960.bp2 | 102960de1 | \([0, 0, 0, -11883, -4276582]\) | \(-62146192681/2610036000\) | \(-7793525735424000\) | \([]\) | \(414720\) | \(1.7294\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.bp do not have complex multiplication.Modular form 102960.2.a.bp
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.