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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 28798m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28798.m2 | 28798m1 | \([1, 1, 0, -2180, 38108]\) | \(647214625/3332\) | \(5902841252\) | \([2]\) | \(22400\) | \(0.72077\) | \(\Gamma_0(N)\)-optimal |
28798.m1 | 28798m2 | \([1, 1, 0, -3390, -10534]\) | \(2433138625/1387778\) | \(2458533381458\) | \([2]\) | \(44800\) | \(1.0673\) |
Rank
sage: E.rank()
The elliptic curves in class 28798m have rank \(0\).
Complex multiplication
The elliptic curves in class 28798m do not have complex multiplication.Modular form 28798.2.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 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.