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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 10626.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10626.o1 | 10626s2 | \([1, 0, 0, -16380, 254016]\) | \(486034459476995521/253095136942032\) | \(253095136942032\) | \([2]\) | \(55296\) | \(1.4556\) | |
10626.o2 | 10626s1 | \([1, 0, 0, 3860, 31376]\) | \(6360314548472639/4097346156288\) | \(-4097346156288\) | \([2]\) | \(27648\) | \(1.1090\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10626.o have rank \(1\).
Complex multiplication
The elliptic curves in class 10626.o do not have complex multiplication.Modular form 10626.2.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.