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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 39600bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.m3 | 39600bh1 | \([0, 0, 0, -768450, 259160875]\) | \(275361373935616/148240125\) | \(27016762781250000\) | \([2]\) | \(589824\) | \(2.1021\) | \(\Gamma_0(N)\)-optimal |
| 39600.m2 | 39600bh2 | \([0, 0, 0, -904575, 161014750]\) | \(28071778927696/12404390625\) | \(36171203062500000000\) | \([2, 2]\) | \(1179648\) | \(2.4486\) | |
| 39600.m4 | 39600bh3 | \([0, 0, 0, 3104925, 1199475250]\) | \(283811208976796/217529296875\) | \(-2537261718750000000000\) | \([2]\) | \(2359296\) | \(2.7952\) | |
| 39600.m1 | 39600bh4 | \([0, 0, 0, -7092075, -7158797750]\) | \(3382175663521924/59189241375\) | \(690383311398000000000\) | \([2]\) | \(2359296\) | \(2.7952\) |
Rank
sage: E.rank()
The elliptic curves in class 39600bh have rank \(1\).
Complex multiplication
The elliptic curves in class 39600bh do not have complex multiplication.Modular form 39600.2.a.bh
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.
