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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 190608.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190608.z1 | 190608bv1 | \([0, -1, 0, -84650288, 254746408896]\) | \(348118804674069625/56004830035968\) | \(10792126747842053111021568\) | \([2]\) | \(43130880\) | \(3.5256\) | \(\Gamma_0(N)\)-optimal |
190608.z2 | 190608bv2 | \([0, -1, 0, 151934672, 1423097575360]\) | \(2012856588372458375/5705334819790848\) | \(-1099417612275862240858472448\) | \([2]\) | \(86261760\) | \(3.8722\) |
Rank
sage: E.rank()
The elliptic curves in class 190608.z have rank \(0\).
Complex multiplication
The elliptic curves in class 190608.z do not have complex multiplication.Modular form 190608.2.a.z
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.