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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 405042.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405042.bb1 | 405042bb1 | \([1, 1, 0, -70763, 7211325]\) | \(832972004929/610368\) | \(28715300294208\) | \([2]\) | \(2764800\) | \(1.5166\) | \(\Gamma_0(N)\)-optimal |
405042.bb2 | 405042bb2 | \([1, 1, 0, -56323, 10258165]\) | \(-420021471169/727634952\) | \(-34232227363232712\) | \([2]\) | \(5529600\) | \(1.8632\) |
Rank
sage: E.rank()
The elliptic curves in class 405042.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 405042.bb do not have complex multiplication.Modular form 405042.2.a.bb
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.