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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 48400bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48400.ce1 | 48400bz1 | \([0, 1, 0, -4284408, 3444543188]\) | \(-76711450249/851840\) | \(-96581537423360000000\) | \([]\) | \(1935360\) | \(2.6496\) | \(\Gamma_0(N)\)-optimal |
48400.ce2 | 48400bz2 | \([0, 1, 0, 14349592, 17867259188]\) | \(2882081488391/2883584000\) | \(-326940477095936000000000\) | \([]\) | \(5806080\) | \(3.1989\) |
Rank
sage: E.rank()
The elliptic curves in class 48400bz have rank \(1\).
Complex multiplication
The elliptic curves in class 48400bz do not have complex multiplication.Modular form 48400.2.a.bz
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 Cremona 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 Cremona labels.