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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 11466bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11466.cj4 | 11466bz1 | \([1, -1, 1, -8609, 6420593]\) | \(-822656953/207028224\) | \(-17756007709999104\) | \([2]\) | \(92160\) | \(1.7972\) | \(\Gamma_0(N)\)-optimal |
| 11466.cj3 | 11466bz2 | \([1, -1, 1, -573089, 165603953]\) | \(242702053576633/2554695936\) | \(219106360765184256\) | \([2, 2]\) | \(184320\) | \(2.1438\) | |
| 11466.cj2 | 11466bz3 | \([1, -1, 1, -1031729, -136548079]\) | \(1416134368422073/725251155408\) | \(62201978350112332368\) | \([2]\) | \(368640\) | \(2.4903\) | |
| 11466.cj1 | 11466bz4 | \([1, -1, 1, -9146129, 10648717265]\) | \(986551739719628473/111045168\) | \(9523913315153328\) | \([2]\) | \(368640\) | \(2.4903\) |
Rank
sage: E.rank()
The elliptic curves in class 11466bz have rank \(0\).
Complex multiplication
The elliptic curves in class 11466bz do not have complex multiplication.Modular form 11466.2.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.
