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SageMath
E = EllipticCurve("mv1")
E.isogeny_class()
Elliptic curves in class 486720mv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 486720.mv3 | 486720mv1 | \([0, 0, 0, -1316172, 563732624]\) | \(273359449/9360\) | \(8633828403566346240\) | \([2]\) | \(8257536\) | \(2.4054\) | \(\Gamma_0(N)\)-optimal |
| 486720.mv2 | 486720mv2 | \([0, 0, 0, -3263052, -1491393904]\) | \(4165509529/1368900\) | \(1262697404021578137600\) | \([2, 2]\) | \(16515072\) | \(2.7520\) | |
| 486720.mv4 | 486720mv3 | \([0, 0, 0, 9391668, -10243398256]\) | \(99317171591/106616250\) | \(-98344701659372912640000\) | \([2]\) | \(33030144\) | \(3.0985\) | |
| 486720.mv1 | 486720mv4 | \([0, 0, 0, -47067852, -124267487344]\) | \(12501706118329/2570490\) | \(2371065125329407836160\) | \([2]\) | \(33030144\) | \(3.0985\) |
Rank
sage: E.rank()
The elliptic curves in class 486720mv have rank \(0\).
Complex multiplication
The elliptic curves in class 486720mv do not have complex multiplication.Modular form 486720.2.a.mv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
