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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 3600.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3600.bj1 | 3600z4 | \([0, 0, 0, -87075, 2585250]\) | \(57960603/31250\) | \(39366000000000000\) | \([2]\) | \(27648\) | \(1.8754\) | |
3600.bj2 | 3600z2 | \([0, 0, 0, -51075, -4442750]\) | \(8527173507/200\) | \(345600000000\) | \([2]\) | \(9216\) | \(1.3261\) | |
3600.bj3 | 3600z1 | \([0, 0, 0, -3075, -74750]\) | \(-1860867/320\) | \(-552960000000\) | \([2]\) | \(4608\) | \(0.97950\) | \(\Gamma_0(N)\)-optimal |
3600.bj4 | 3600z3 | \([0, 0, 0, 20925, 317250]\) | \(804357/500\) | \(-629856000000000\) | \([2]\) | \(13824\) | \(1.5288\) |
Rank
sage: E.rank()
The elliptic curves in class 3600.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 3600.bj do not have complex multiplication.Modular form 3600.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.