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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 171600bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
171600.gl1 | 171600bz1 | \([0, 1, 0, -2309760408, -42772804936812]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-1677514808812877438976000000\) | \([]\) | \(118540800\) | \(4.1337\) | \(\Gamma_0(N)\)-optimal |
171600.gl2 | 171600bz2 | \([0, 1, 0, 6541235592, 2684357180335188]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-3130801712418763376350321536000000\) | \([]\) | \(829785600\) | \(5.1066\) |
Rank
sage: E.rank()
The elliptic curves in class 171600bz have rank \(0\).
Complex multiplication
The elliptic curves in class 171600bz do not have complex multiplication.Modular form 171600.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.