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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 179520fy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179520.eu2 | 179520fy1 | \([0, 1, 0, -12801, -481185]\) | \(885012508801/137332800\) | \(36000969523200\) | \([2]\) | \(442368\) | \(1.3245\) | \(\Gamma_0(N)\)-optimal |
179520.eu1 | 179520fy2 | \([0, 1, 0, -56321, 4662879]\) | \(75370704203521/7497765000\) | \(1965494108160000\) | \([2]\) | \(884736\) | \(1.6711\) |
Rank
sage: E.rank()
The elliptic curves in class 179520fy have rank \(1\).
Complex multiplication
The elliptic curves in class 179520fy do not have complex multiplication.Modular form 179520.2.a.fy
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.