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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 3600.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3600.ba1 | 3600ba4 | \([0, 0, 0, -459675, 119954250]\) | \(8527173507/200\) | \(251942400000000\) | \([2]\) | \(27648\) | \(1.8754\) | |
3600.ba2 | 3600ba3 | \([0, 0, 0, -27675, 2018250]\) | \(-1860867/320\) | \(-403107840000000\) | \([2]\) | \(13824\) | \(1.5288\) | |
3600.ba3 | 3600ba2 | \([0, 0, 0, -9675, -95750]\) | \(57960603/31250\) | \(54000000000000\) | \([2]\) | \(9216\) | \(1.3261\) | |
3600.ba4 | 3600ba1 | \([0, 0, 0, 2325, -11750]\) | \(804357/500\) | \(-864000000000\) | \([2]\) | \(4608\) | \(0.97950\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3600.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 3600.ba do not have complex multiplication.Modular form 3600.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.