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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 59290o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.bj2 | 59290o1 | \([1, 0, 1, 59166, -22356204]\) | \(109902239/1100000\) | \(-229264618097900000\) | \([]\) | \(792000\) | \(2.0123\) | \(\Gamma_0(N)\)-optimal |
59290.bj1 | 59290o2 | \([1, 0, 1, -35218384, -80448529724]\) | \(-23178622194826561/1610510\) | \(-335666327357135390\) | \([]\) | \(3960000\) | \(2.8170\) |
Rank
sage: E.rank()
The elliptic curves in class 59290o have rank \(1\).
Complex multiplication
The elliptic curves in class 59290o do not have complex multiplication.Modular form 59290.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.