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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 33813o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33813.e4 | 33813o1 | \([1, -1, 1, 1246, 35768]\) | \(12167/39\) | \(-686255224239\) | \([2]\) | \(40960\) | \(0.95440\) | \(\Gamma_0(N)\)-optimal |
33813.e3 | 33813o2 | \([1, -1, 1, -11759, 425918]\) | \(10218313/1521\) | \(26763953745321\) | \([2, 2]\) | \(81920\) | \(1.3010\) | |
33813.e2 | 33813o3 | \([1, -1, 1, -50774, -3974974]\) | \(822656953/85683\) | \(1507702727653083\) | \([2]\) | \(163840\) | \(1.6475\) | |
33813.e1 | 33813o4 | \([1, -1, 1, -180824, 29640350]\) | \(37159393753/1053\) | \(18528891054453\) | \([2]\) | \(163840\) | \(1.6475\) |
Rank
sage: E.rank()
The elliptic curves in class 33813o have rank \(1\).
Complex multiplication
The elliptic curves in class 33813o do not have complex multiplication.Modular form 33813.2.a.o
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.