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SageMath
E = EllipticCurve("gz1")
E.isogeny_class()
Elliptic curves in class 91200gz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91200.m2 | 91200gz1 | \([0, -1, 0, -993, -12543]\) | \(-13231796/1083\) | \(-8871936000\) | \([2]\) | \(69632\) | \(0.65481\) | \(\Gamma_0(N)\)-optimal |
91200.m1 | 91200gz2 | \([0, -1, 0, -16193, -787743]\) | \(28662399178/171\) | \(2801664000\) | \([2]\) | \(139264\) | \(1.0014\) |
Rank
sage: E.rank()
The elliptic curves in class 91200gz have rank \(1\).
Complex multiplication
The elliptic curves in class 91200gz do not have complex multiplication.Modular form 91200.2.a.gz
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 Cremona 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 Cremona labels.