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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 97104.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97104.g1 | 97104bk4 | \([0, -1, 0, -609784, 165115888]\) | \(1246079601667529/137282971014\) | \(2762634185079939072\) | \([2]\) | \(1536000\) | \(2.2719\) | |
97104.g2 | 97104bk2 | \([0, -1, 0, -139224, -19948560]\) | \(14830727012009/4704\) | \(94661640192\) | \([2]\) | \(307200\) | \(1.4672\) | |
97104.g3 | 97104bk1 | \([0, -1, 0, -8664, -312336]\) | \(-3574558889/64512\) | \(-1298216779776\) | \([2]\) | \(153600\) | \(1.1207\) | \(\Gamma_0(N)\)-optimal |
97104.g4 | 97104bk3 | \([0, -1, 0, 51176, 12830704]\) | \(736558976791/3969746172\) | \(-79885774614675456\) | \([2]\) | \(768000\) | \(1.9254\) |
Rank
sage: E.rank()
The elliptic curves in class 97104.g have rank \(0\).
Complex multiplication
The elliptic curves in class 97104.g do not have complex multiplication.Modular form 97104.2.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.
\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.