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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 24150bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24150.by4 | 24150bt1 | \([1, 1, 1, -85228938, -264087492969]\) | \(4381924769947287308715481/608122186185572352000\) | \(9501909159149568000000000\) | \([4]\) | \(7741440\) | \(3.5193\) | \(\Gamma_0(N)\)-optimal |
| 24150.by2 | 24150bt2 | \([1, 1, 1, -1314540938, -18344808388969]\) | \(16077778198622525072705635801/388799208512064000000\) | \(6074987633001000000000000\) | \([2, 2]\) | \(15482880\) | \(3.8659\) | |
| 24150.by3 | 24150bt3 | \([1, 1, 1, -1265540938, -19775412388969]\) | \(-14346048055032350809895395801/2509530875136386550792000\) | \(-39211419924006039856125000000\) | \([2]\) | \(30965760\) | \(4.2124\) | |
| 24150.by1 | 24150bt4 | \([1, 1, 1, -21032532938, -1174055755492969]\) | \(65853432878493908038433301506521/38511703125000000\) | \(601745361328125000000\) | \([2]\) | \(30965760\) | \(4.2124\) |
Rank
sage: E.rank()
The elliptic curves in class 24150bt have rank \(1\).
Complex multiplication
The elliptic curves in class 24150bt do not have complex multiplication.Modular form 24150.2.a.bt
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.
