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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 3600.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3600.l1 | 3600bo2 | \([0, 0, 0, -18075, -935350]\) | \(-349938025/8\) | \(-14929920000\) | \([]\) | \(4320\) | \(1.0657\) | |
3600.l2 | 3600bo3 | \([0, 0, 0, -10875, 526250]\) | \(-121945/32\) | \(-37324800000000\) | \([]\) | \(7200\) | \(1.3211\) | |
3600.l3 | 3600bo1 | \([0, 0, 0, -75, -2950]\) | \(-25/2\) | \(-3732480000\) | \([]\) | \(1440\) | \(0.51635\) | \(\Gamma_0(N)\)-optimal |
3600.l4 | 3600bo4 | \([0, 0, 0, 79125, -3883750]\) | \(46969655/32768\) | \(-38220595200000000\) | \([]\) | \(21600\) | \(1.8704\) |
Rank
sage: E.rank()
The elliptic curves in class 3600.l have rank \(0\).
Complex multiplication
The elliptic curves in class 3600.l do not have complex multiplication.Modular form 3600.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.