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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 254100.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.z1 | 254100z2 | \([0, -1, 0, -174688708, 888441265912]\) | \(665567485783184/257298363\) | \(227909872627321500000000\) | \([2]\) | \(51609600\) | \(3.4473\) | |
254100.z2 | 254100z1 | \([0, -1, 0, -9296833, 18149219662]\) | \(-1605176213504/1640558367\) | \(-90823413162527718750000\) | \([2]\) | \(25804800\) | \(3.1007\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254100.z have rank \(0\).
Complex multiplication
The elliptic curves in class 254100.z do not have complex multiplication.Modular form 254100.2.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.