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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 32490.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32490.g1 | 32490h2 | \([1, -1, 0, -2185020, -743134604]\) | \(4904335099/1822500\) | \(428723681988423847500\) | \([2]\) | \(1167360\) | \(2.6589\) | |
32490.g2 | 32490h1 | \([1, -1, 0, -950400, 348516400]\) | \(403583419/10800\) | \(2540584782153622800\) | \([2]\) | \(583680\) | \(2.3123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32490.g have rank \(0\).
Complex multiplication
The elliptic curves in class 32490.g do not have complex multiplication.Modular form 32490.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.