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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 16900.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16900.g1 | 16900g2 | \([0, -1, 0, -2139258, -1203609863]\) | \(151635187115776/25\) | \(178506250000\) | \([]\) | \(124416\) | \(2.0018\) | |
16900.g2 | 16900g1 | \([0, -1, 0, -26758, -1597363]\) | \(296747776/15625\) | \(111566406250000\) | \([]\) | \(41472\) | \(1.4525\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16900.g have rank \(0\).
Complex multiplication
The elliptic curves in class 16900.g do not have complex multiplication.Modular form 16900.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.