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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 200400bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200400.w2 | 200400bm1 | \([0, -1, 0, -2147008, 2679872512]\) | \(-17101922279625721/38553753600000\) | \(-2467440230400000000000\) | \([2]\) | \(8709120\) | \(2.7934\) | \(\Gamma_0(N)\)-optimal |
| 200400.w1 | 200400bm2 | \([0, -1, 0, -44899008, 115716160512]\) | \(156406207396688718841/152178750000000\) | \(9739440000000000000000\) | \([2]\) | \(17418240\) | \(3.1399\) |
Rank
sage: E.rank()
The elliptic curves in class 200400bm have rank \(0\).
Complex multiplication
The elliptic curves in class 200400bm do not have complex multiplication.Modular form 200400.2.a.bm
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
