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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2178.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2178.g1 | 2178k3 | \([1, -1, 1, -383351, -91261299]\) | \(4824238966273/66\) | \(85236885954\) | \([2]\) | \(15360\) | \(1.6533\) | |
2178.g2 | 2178k2 | \([1, -1, 1, -23981, -1418799]\) | \(1180932193/4356\) | \(5625634472964\) | \([2, 2]\) | \(7680\) | \(1.3067\) | |
2178.g3 | 2178k4 | \([1, -1, 1, -13091, -2721243]\) | \(-192100033/2371842\) | \(-3063157970528898\) | \([2]\) | \(15360\) | \(1.6533\) | |
2178.g4 | 2178k1 | \([1, -1, 1, -2201, 1257]\) | \(912673/528\) | \(681895087632\) | \([4]\) | \(3840\) | \(0.96015\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2178.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2178.g do not have complex multiplication.Modular form 2178.2.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.