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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 161874m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161874.bu2 | 161874m1 | \([1, -1, 1, -1216535, 516570095]\) | \(1845026709625/793152\) | \(85595506884021312\) | \([2]\) | \(2280960\) | \(2.2092\) | \(\Gamma_0(N)\)-optimal |
| 161874.bu3 | 161874m2 | \([1, -1, 1, -1026095, 683624063]\) | \(-1107111813625/1228691592\) | \(-132598139601709514952\) | \([2]\) | \(4561920\) | \(2.5557\) | |
| 161874.bu1 | 161874m3 | \([1, -1, 1, -3573230, -1964644099]\) | \(46753267515625/11591221248\) | \(1250903304949616345088\) | \([2]\) | \(6842880\) | \(2.7585\) | |
| 161874.bu4 | 161874m4 | \([1, -1, 1, 8614930, -12465962755]\) | \(655215969476375/1001033261568\) | \(-108029670771400753771008\) | \([2]\) | \(13685760\) | \(3.1051\) |
Rank
sage: E.rank()
The elliptic curves in class 161874m have rank \(0\).
Complex multiplication
The elliptic curves in class 161874m do not have complex multiplication.Modular form 161874.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
