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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 236600bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236600.bh1 | 236600bh1 | \([0, 0, 0, -57134675, 166224470750]\) | \(267080942160036/1990625\) | \(153733866650000000000\) | \([2]\) | \(18063360\) | \(3.0494\) | \(\Gamma_0(N)\)-optimal |
| 236600.bh2 | 236600bh2 | \([0, 0, 0, -55951675, 173437221750]\) | \(-125415986034978/11552734375\) | \(-1784410952187500000000000\) | \([2]\) | \(36126720\) | \(3.3960\) |
Rank
sage: E.rank()
The elliptic curves in class 236600bh have rank \(0\).
Complex multiplication
The elliptic curves in class 236600bh do not have complex multiplication.Modular form 236600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
