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SageMath
E = EllipticCurve("lw1")
E.isogeny_class()
Elliptic curves in class 446400.lw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446400.lw1 | 446400lw3 | \([0, 0, 0, -95450700, 358929466000]\) | \(32208729120020809/658986840\) | \(1967724160450560000000\) | \([2]\) | \(42467328\) | \(3.2055\) | \(\Gamma_0(N)\)-optimal* |
446400.lw2 | 446400lw2 | \([0, 0, 0, -6170700, 5202106000]\) | \(8702409880009/1120910400\) | \(3347020519833600000000\) | \([2, 2]\) | \(21233664\) | \(2.8589\) | \(\Gamma_0(N)\)-optimal* |
446400.lw3 | 446400lw1 | \([0, 0, 0, -1562700, -668486000]\) | \(141339344329/17141760\) | \(51185021091840000000\) | \([2]\) | \(10616832\) | \(2.5123\) | \(\Gamma_0(N)\)-optimal* |
446400.lw4 | 446400lw4 | \([0, 0, 0, 9381300, 27192634000]\) | \(30579142915511/124675335000\) | \(-372278555504640000000000\) | \([2]\) | \(42467328\) | \(3.2055\) |
Rank
sage: E.rank()
The elliptic curves in class 446400.lw have rank \(0\).
Complex multiplication
The elliptic curves in class 446400.lw do not have complex multiplication.Modular form 446400.2.a.lw
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.