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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 39600.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.g1 | 39600cb3 | \([0, 0, 0, -38643075, 92460197250]\) | \(5066026756449723/11000000\) | \(13856832000000000000\) | \([2]\) | \(2985984\) | \(2.9198\) | |
| 39600.g2 | 39600cb4 | \([0, 0, 0, -38211075, 94628405250]\) | \(-4898016158612283/236328125000\) | \(-297705375000000000000000\) | \([2]\) | \(5971968\) | \(3.2663\) | |
| 39600.g3 | 39600cb1 | \([0, 0, 0, -627075, 40485250]\) | \(15781142246787/8722841600\) | \(15073070284800000000\) | \([2]\) | \(995328\) | \(2.3705\) | \(\Gamma_0(N)\)-optimal |
| 39600.g4 | 39600cb2 | \([0, 0, 0, 2444925, 320037250]\) | \(935355271080573/566899520000\) | \(-979602370560000000000\) | \([2]\) | \(1990656\) | \(2.7170\) |
Rank
sage: E.rank()
The elliptic curves in class 39600.g have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.g do not have complex multiplication.Modular form 39600.2.a.g
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.
