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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 30926k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30926.m2 | 30926k1 | \([1, 0, 0, 1, 17]\) | \(47/56\) | \(-123704\) | \([]\) | \(4992\) | \(-0.34387\) | \(\Gamma_0(N)\)-optimal |
30926.m1 | 30926k2 | \([1, 0, 0, -469, 3871]\) | \(-5165405233/686\) | \(-1515374\) | \([]\) | \(14976\) | \(0.20544\) |
Rank
sage: E.rank()
The elliptic curves in class 30926k have rank \(0\).
Complex multiplication
The elliptic curves in class 30926k do not have complex multiplication.Modular form 30926.2.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.