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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 141570.ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.ew1 | 141570cj4 | \([1, -1, 1, -547427, -93242069]\) | \(520300455507/193072360\) | \(6732362753259394680\) | \([2]\) | \(4976640\) | \(2.3128\) | |
141570.ew2 | 141570cj2 | \([1, -1, 1, -483902, -129442849]\) | \(261984288445803/42250\) | \(2020908210750\) | \([2]\) | \(1658880\) | \(1.7634\) | |
141570.ew3 | 141570cj1 | \([1, -1, 1, -30152, -2029849]\) | \(-63378025803/812500\) | \(-38863619437500\) | \([2]\) | \(829440\) | \(1.4169\) | \(\Gamma_0(N)\)-optimal |
141570.ew4 | 141570cj3 | \([1, -1, 1, 105973, -10390949]\) | \(3774555693/3515200\) | \(-122573741524977600\) | \([2]\) | \(2488320\) | \(1.9662\) |
Rank
sage: E.rank()
The elliptic curves in class 141570.ew have rank \(0\).
Complex multiplication
The elliptic curves in class 141570.ew do not have complex multiplication.Modular form 141570.2.a.ew
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.