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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 11200.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11200.bz1 | 11200o3 | \([0, 0, 0, -8300, 282000]\) | \(123505992/4375\) | \(2240000000000\) | \([2]\) | \(18432\) | \(1.1405\) | |
| 11200.bz2 | 11200o2 | \([0, 0, 0, -1300, -12000]\) | \(3796416/1225\) | \(78400000000\) | \([2, 2]\) | \(9216\) | \(0.79389\) | |
| 11200.bz3 | 11200o1 | \([0, 0, 0, -1175, -15500]\) | \(179406144/35\) | \(35000000\) | \([2]\) | \(4608\) | \(0.44731\) | \(\Gamma_0(N)\)-optimal |
| 11200.bz4 | 11200o4 | \([0, 0, 0, 3700, -82000]\) | \(10941048/12005\) | \(-6146560000000\) | \([2]\) | \(18432\) | \(1.1405\) |
Rank
sage: E.rank()
The elliptic curves in class 11200.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 11200.bz do not have complex multiplication.Modular form 11200.2.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 LMFDB 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 LMFDB labels.
