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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 397800.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.bm1 | 397800bm2 | \([0, 0, 0, -18910875, -16246764250]\) | \(64122592551794500/27331783704693\) | \(318797925131539152000000\) | \([2]\) | \(42467328\) | \(3.2065\) | |
| 397800.bm2 | 397800bm1 | \([0, 0, 0, -9024375, 10258942250]\) | \(27873248949250000/538367795433\) | \(1569880491482628000000\) | \([2]\) | \(21233664\) | \(2.8599\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397800.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.bm do not have complex multiplication.Modular form 397800.2.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 LMFDB 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 LMFDB labels.
