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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 43890.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43890.m1 | 43890m4 | \([1, 1, 0, -356702, -82147404]\) | \(5019289526512451088361/13006889280\) | \(13006889280\) | \([2]\) | \(319488\) | \(1.6031\) | |
43890.m2 | 43890m2 | \([1, 1, 0, -22302, -1289484]\) | \(1226833350167030761/1972564070400\) | \(1972564070400\) | \([2, 2]\) | \(159744\) | \(1.2565\) | |
43890.m3 | 43890m3 | \([1, 1, 0, -15582, -2073036]\) | \(-418443533445064681/1602744999240000\) | \(-1602744999240000\) | \([4]\) | \(319488\) | \(1.6031\) | |
43890.m4 | 43890m1 | \([1, 1, 0, -1822, -7436]\) | \(669485563505641/368176005120\) | \(368176005120\) | \([2]\) | \(79872\) | \(0.90994\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43890.m have rank \(0\).
Complex multiplication
The elliptic curves in class 43890.m do not have complex multiplication.Modular form 43890.2.a.m
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.