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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 34320.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34320.bs1 | 34320bz2 | \([0, 1, 0, -469216, 123554420]\) | \(2789222297765780449/677605500\) | \(2775472128000\) | \([2]\) | \(221184\) | \(1.7649\) | |
34320.bs2 | 34320bz1 | \([0, 1, 0, -29216, 1938420]\) | \(-673350049820449/10617750000\) | \(-43490304000000\) | \([2]\) | \(110592\) | \(1.4183\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34320.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 34320.bs do not have complex multiplication.Modular form 34320.2.a.bs
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.