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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 432.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
432.g1 | 432e3 | \([0, 0, 0, -1971, 44658]\) | \(-1167051/512\) | \(-371504185344\) | \([]\) | \(432\) | \(0.92725\) | |
432.g2 | 432e1 | \([0, 0, 0, -51, -142]\) | \(-132651/2\) | \(-221184\) | \([]\) | \(48\) | \(-0.17136\) | \(\Gamma_0(N)\)-optimal |
432.g3 | 432e2 | \([0, 0, 0, 189, -702]\) | \(9261/8\) | \(-644972544\) | \([]\) | \(144\) | \(0.37794\) |
Rank
sage: E.rank()
The elliptic curves in class 432.g have rank \(0\).
Complex multiplication
The elliptic curves in class 432.g do not have complex multiplication.Modular form 432.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.