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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1764.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1764.g1 | 1764f4 | \([0, 0, 0, -806295, -278668978]\) | \(2640279346000/3087\) | \(67778563974912\) | \([2]\) | \(13824\) | \(1.9371\) | |
1764.g2 | 1764f3 | \([0, 0, 0, -49980, -4429159]\) | \(-10061824000/352947\) | \(-484334321737392\) | \([2]\) | \(6912\) | \(1.5905\) | |
1764.g3 | 1764f2 | \([0, 0, 0, -12495, -172186]\) | \(9826000/5103\) | \(112042115958528\) | \([2]\) | \(4608\) | \(1.3878\) | |
1764.g4 | 1764f1 | \([0, 0, 0, 2940, -20923]\) | \(2048000/1323\) | \(-1815497249328\) | \([2]\) | \(2304\) | \(1.0412\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1764.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1764.g do not have complex multiplication.Modular form 1764.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.