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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 238260.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
238260.e1 | 238260e4 | \([0, -1, 0, -90248676, 330026613960]\) | \(6749703004355978704/5671875\) | \(68310619212000000\) | \([2]\) | \(12317184\) | \(2.9658\) | |
238260.e2 | 238260e3 | \([0, -1, 0, -5639301, 5160457710]\) | \(-26348629355659264/24169921875\) | \(-18193524292968750000\) | \([2]\) | \(6158592\) | \(2.6192\) | |
238260.e3 | 238260e2 | \([0, -1, 0, -1139436, 431453736]\) | \(13584145739344/1195803675\) | \(14401955172713644800\) | \([2]\) | \(4105728\) | \(2.4165\) | |
238260.e4 | 238260e1 | \([0, -1, 0, 78939, 31339386]\) | \(72268906496/606436875\) | \(-456485712884190000\) | \([2]\) | \(2052864\) | \(2.0699\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 238260.e have rank \(0\).
Complex multiplication
The elliptic curves in class 238260.e do not have complex multiplication.Modular form 238260.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.