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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 179088.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179088.j1 | 179088ce2 | \([0, -1, 0, -62704, -5898896]\) | \(26626643276635588/624749014071\) | \(639742990408704\) | \([2]\) | \(798720\) | \(1.6266\) | |
179088.j2 | 179088ce1 | \([0, -1, 0, 476, -288512]\) | \(46493463728/140338628703\) | \(-35926688947968\) | \([2]\) | \(399360\) | \(1.2800\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179088.j have rank \(0\).
Complex multiplication
The elliptic curves in class 179088.j do not have complex multiplication.Modular form 179088.2.a.j
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.