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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 22800bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22800.x4 | 22800bz1 | \([0, -1, 0, -140808, 18320112]\) | \(4824238966273/537919488\) | \(34426847232000000\) | \([2]\) | \(184320\) | \(1.9062\) | \(\Gamma_0(N)\)-optimal |
| 22800.x2 | 22800bz2 | \([0, -1, 0, -2188808, 1247120112]\) | \(18120364883707393/269485056\) | \(17247043584000000\) | \([2, 2]\) | \(368640\) | \(2.2527\) | |
| 22800.x3 | 22800bz3 | \([0, -1, 0, -2124808, 1323408112]\) | \(-16576888679672833/2216253521952\) | \(-141840225404928000000\) | \([2]\) | \(737280\) | \(2.5993\) | |
| 22800.x1 | 22800bz4 | \([0, -1, 0, -35020808, 79781264112]\) | \(74220219816682217473/16416\) | \(1050624000000\) | \([2]\) | \(737280\) | \(2.5993\) |
Rank
sage: E.rank()
The elliptic curves in class 22800bz have rank \(1\).
Complex multiplication
The elliptic curves in class 22800bz do not have complex multiplication.Modular form 22800.2.a.bz
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.
