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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 192960.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
192960.bc1 | 192960bj2 | \([0, 0, 0, -108048, -15099122]\) | \(-2989967081734144/380653171875\) | \(-17759754387000000\) | \([]\) | \(1658880\) | \(1.8518\) | |
192960.bc2 | 192960bj1 | \([0, 0, 0, 8592, 46582]\) | \(1503484706816/890163675\) | \(-41531476420800\) | \([]\) | \(552960\) | \(1.3025\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 192960.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 192960.bc do not have complex multiplication.Modular form 192960.2.a.bc
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.