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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 145794k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145794.bc4 | 145794k1 | \([1, 1, 1, -4464, -3903]\) | \(912673/528\) | \(5691425693712\) | \([2]\) | \(397440\) | \(1.1370\) | \(\Gamma_0(N)\)-optimal |
| 145794.bc2 | 145794k2 | \([1, 1, 1, -48644, 4096001]\) | \(1180932193/4356\) | \(46954261973124\) | \([2, 2]\) | \(794880\) | \(1.4835\) | |
| 145794.bc1 | 145794k3 | \([1, 1, 1, -777614, 263609321]\) | \(4824238966273/66\) | \(711428211714\) | \([2]\) | \(1589760\) | \(1.8301\) | |
| 145794.bc3 | 145794k4 | \([1, 1, 1, -26554, 7860137]\) | \(-192100033/2371842\) | \(-25566595644366018\) | \([2]\) | \(1589760\) | \(1.8301\) |
Rank
sage: E.rank()
The elliptic curves in class 145794k have rank \(0\).
Complex multiplication
The elliptic curves in class 145794k do not have complex multiplication.Modular form 145794.2.a.k
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.
