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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 430950.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.bc1 | 430950bc2 | \([1, 1, 0, -112756400, -460916448000]\) | \(-60039987383782546728601/2882975793315840\) | \(-7612857954224640000000\) | \([]\) | \(63452160\) | \(3.2718\) | |
430950.bc2 | 430950bc1 | \([1, 1, 0, -217025, -1655104875]\) | \(-428104115567401/447858085284000\) | \(-1182625256453062500000\) | \([]\) | \(21150720\) | \(2.7225\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 430950.bc do not have complex multiplication.Modular form 430950.2.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.