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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 91035.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91035.o1 | 91035a2 | \([1, -1, 1, -30833, -2057748]\) | \(4973940243/50575\) | \(32960453908725\) | \([2]\) | \(221184\) | \(1.4116\) | |
91035.o2 | 91035a1 | \([1, -1, 1, -488, -79254]\) | \(-19683/4165\) | \(-2714390321895\) | \([2]\) | \(110592\) | \(1.0651\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.o have rank \(0\).
Complex multiplication
The elliptic curves in class 91035.o do not have complex multiplication.Modular form 91035.2.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 LMFDB 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 LMFDB labels.