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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 141288.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141288.g1 | 141288m3 | \([0, -1, 0, -128112, 17669628]\) | \(381775972/567\) | \(345359178759168\) | \([2]\) | \(774144\) | \(1.6906\) | |
141288.g2 | 141288m2 | \([0, -1, 0, -10372, 102820]\) | \(810448/441\) | \(67153173647616\) | \([2, 2]\) | \(387072\) | \(1.3440\) | |
141288.g3 | 141288m1 | \([0, -1, 0, -6167, -183120]\) | \(2725888/21\) | \(199860635856\) | \([2]\) | \(193536\) | \(0.99746\) | \(\Gamma_0(N)\)-optimal |
141288.g4 | 141288m4 | \([0, -1, 0, 40088, 768892]\) | \(11696828/7203\) | \(-4387340678310912\) | \([2]\) | \(774144\) | \(1.6906\) |
Rank
sage: E.rank()
The elliptic curves in class 141288.g have rank \(0\).
Complex multiplication
The elliptic curves in class 141288.g do not have complex multiplication.Modular form 141288.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.