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SageMath
E = EllipticCurve("gg1")
E.isogeny_class()
Elliptic curves in class 193600.gg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.gg1 | 193600dq2 | \([0, 1, 0, -1149988033, -15010640095937]\) | \(-23178622194826561/1610510\) | \(-11686366028226560000000\) | \([]\) | \(55296000\) | \(3.6885\) | |
| 193600.gg2 | 193600dq1 | \([0, 1, 0, 1931967, -4171695937]\) | \(109902239/1100000\) | \(-7981945241600000000000\) | \([]\) | \(11059200\) | \(2.8837\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193600.gg have rank \(1\).
Complex multiplication
The elliptic curves in class 193600.gg do not have complex multiplication.Modular form 193600.2.a.gg
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
