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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 79350.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79350.o1 | 79350b2 | \([1, 1, 0, -51908400, 143926020000]\) | \(6687281588245201/165600\) | \(383042862787500000\) | \([2]\) | \(6082560\) | \(2.8924\) | |
79350.o2 | 79350b1 | \([1, 1, 0, -3240400, 2253472000]\) | \(-1626794704081/8125440\) | \(-18794636467440000000\) | \([2]\) | \(3041280\) | \(2.5458\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79350.o have rank \(0\).
Complex multiplication
The elliptic curves in class 79350.o do not have complex multiplication.Modular form 79350.2.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.