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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 132600.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
132600.g1 | 132600s2 | \([0, -1, 0, -38708, 1337412]\) | \(1603530178000/738501777\) | \(2954007108000000\) | \([2]\) | \(663552\) | \(1.6632\) | |
132600.g2 | 132600s1 | \([0, -1, 0, -19583, -1034088]\) | \(3322336000000/51429573\) | \(12857393250000\) | \([2]\) | \(331776\) | \(1.3167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 132600.g have rank \(1\).
Complex multiplication
The elliptic curves in class 132600.g do not have complex multiplication.Modular form 132600.2.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.