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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 11466y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11466.z3 | 11466y1 | \([1, -1, 0, -3096, -58640]\) | \(38272753/4368\) | \(374626416528\) | \([2]\) | \(18432\) | \(0.95309\) | \(\Gamma_0(N)\)-optimal |
11466.z2 | 11466y2 | \([1, -1, 0, -11916, 440572]\) | \(2181825073/298116\) | \(25568252928036\) | \([2, 2]\) | \(36864\) | \(1.2997\) | |
11466.z1 | 11466y3 | \([1, -1, 0, -183906, 30401230]\) | \(8020417344913/187278\) | \(16062107608638\) | \([2]\) | \(73728\) | \(1.6462\) | |
11466.z4 | 11466y4 | \([1, -1, 0, 18954, 2323642]\) | \(8780064047/32388174\) | \(-2777808050253054\) | \([2]\) | \(73728\) | \(1.6462\) |
Rank
sage: E.rank()
The elliptic curves in class 11466y have rank \(0\).
Complex multiplication
The elliptic curves in class 11466y do not have complex multiplication.Modular form 11466.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.