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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4046.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4046.b1 | 4046c2 | \([1, 0, 1, -37143, -526438]\) | \(234770924809/130960928\) | \(3161078435904032\) | \([2]\) | \(46080\) | \(1.6644\) | |
4046.b2 | 4046c1 | \([1, 0, 1, 9097, -64038]\) | \(3449795831/2071552\) | \(-50002229337088\) | \([2]\) | \(23040\) | \(1.3179\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4046.b have rank \(1\).
Complex multiplication
The elliptic curves in class 4046.b do not have complex multiplication.Modular form 4046.2.a.b
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.