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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 92736.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.bf1 | 92736eq2 | \([0, 0, 0, -137196, 19498320]\) | \(1494447319737/5411854\) | \(1034221405077504\) | \([2]\) | \(589824\) | \(1.7420\) | |
92736.bf2 | 92736eq1 | \([0, 0, 0, -4716, 580176]\) | \(-60698457/725788\) | \(-138700246745088\) | \([2]\) | \(294912\) | \(1.3955\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92736.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 92736.bf do not have complex multiplication.Modular form 92736.2.a.bf
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.