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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 176890.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176890.c1 | 176890cn1 | \([1, -1, 0, -2329420, -1367843660]\) | \(-5154200289/20\) | \(-5424202836693620\) | \([]\) | \(5503680\) | \(2.2323\) | \(\Gamma_0(N)\)-optimal |
176890.c2 | 176890cn2 | \([1, -1, 0, 16244030, 12979774996]\) | \(1747829720511/1280000000\) | \(-347148981548391680000000\) | \([]\) | \(38525760\) | \(3.2053\) |
Rank
sage: E.rank()
The elliptic curves in class 176890.c have rank \(0\).
Complex multiplication
The elliptic curves in class 176890.c do not have complex multiplication.Modular form 176890.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.