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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 128271e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
128271.m2 | 128271e1 | \([1, 1, 0, -3890, -1359873]\) | \(-1349232625/164333367\) | \(-793205774835903\) | \([2]\) | \(368640\) | \(1.5384\) | \(\Gamma_0(N)\)-optimal |
128271.m1 | 128271e2 | \([1, 1, 0, -209225, -36636426]\) | \(209849322390625/1882056627\) | \(9084327865713243\) | \([2]\) | \(737280\) | \(1.8850\) |
Rank
sage: E.rank()
The elliptic curves in class 128271e have rank \(0\).
Complex multiplication
The elliptic curves in class 128271e do not have complex multiplication.Modular form 128271.2.a.e
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 Cremona 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 Cremona labels.