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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 60840.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60840.m1 | 60840h4 | \([0, 0, 0, -856323, 304781022]\) | \(9636491538/8125\) | \(58551896183040000\) | \([2]\) | \(688128\) | \(2.1449\) | |
| 60840.m2 | 60840h2 | \([0, 0, 0, -65403, 2491398]\) | \(8586756/4225\) | \(15223493007590400\) | \([2, 2]\) | \(344064\) | \(1.7983\) | |
| 60840.m3 | 60840h1 | \([0, 0, 0, -34983, -2491398]\) | \(5256144/65\) | \(58551896183040\) | \([2]\) | \(172032\) | \(1.4518\) | \(\Gamma_0(N)\)-optimal |
| 60840.m4 | 60840h3 | \([0, 0, 0, 238797, 19100718]\) | \(208974222/142805\) | \(-1029108127313111040\) | \([2]\) | \(688128\) | \(2.1449\) |
Rank
sage: E.rank()
The elliptic curves in class 60840.m have rank \(0\).
Complex multiplication
The elliptic curves in class 60840.m do not have complex multiplication.Modular form 60840.2.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.
