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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 59150k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59150.k2 | 59150k1 | \([1, 1, 0, 75, -125]\) | \(17303/14\) | \(-36968750\) | \([]\) | \(15552\) | \(0.13997\) | \(\Gamma_0(N)\)-optimal |
59150.k1 | 59150k2 | \([1, 1, 0, -1550, -24500]\) | \(-156116857/2744\) | \(-7245875000\) | \([]\) | \(46656\) | \(0.68928\) |
Rank
sage: E.rank()
The elliptic curves in class 59150k have rank \(0\).
Complex multiplication
The elliptic curves in class 59150k do not have complex multiplication.Modular form 59150.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.