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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 28730k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28730.o2 | 28730k1 | \([1, 0, 1, 67427, -2086472]\) | \(7023836099951/4456448000\) | \(-21510423314432000\) | \([]\) | \(196560\) | \(1.8229\) | \(\Gamma_0(N)\)-optimal |
| 28730.o1 | 28730k2 | \([1, 0, 1, -1122333, -472495944]\) | \(-32391289681150609/1228250000000\) | \(-5928528154250000000\) | \([]\) | \(589680\) | \(2.3722\) |
Rank
sage: E.rank()
The elliptic curves in class 28730k have rank \(0\).
Complex multiplication
The elliptic curves in class 28730k do not have complex multiplication.Modular form 28730.2.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.
