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SageMath
E = EllipticCurve("gg1")
E.isogeny_class()
Elliptic curves in class 333200.gg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333200.gg1 | 333200gg1 | \([0, -1, 0, -1808, 34112]\) | \(-208537/34\) | \(-106624000000\) | \([]\) | \(311040\) | \(0.84362\) | \(\Gamma_0(N)\)-optimal |
333200.gg2 | 333200gg2 | \([0, -1, 0, 12192, -133888]\) | \(63905303/39304\) | \(-123257344000000\) | \([]\) | \(933120\) | \(1.3929\) |
Rank
sage: E.rank()
The elliptic curves in class 333200.gg have rank \(1\).
Complex multiplication
The elliptic curves in class 333200.gg do not have complex multiplication.Modular form 333200.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.