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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 35280k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.b2 | 35280k1 | \([0, 0, 0, -63, -98]\) | \(11664/5\) | \(11854080\) | \([2]\) | \(8192\) | \(0.053805\) | \(\Gamma_0(N)\)-optimal |
| 35280.b1 | 35280k2 | \([0, 0, 0, -483, 4018]\) | \(1314036/25\) | \(237081600\) | \([2]\) | \(16384\) | \(0.40038\) |
Rank
sage: E.rank()
The elliptic curves in class 35280k have rank \(2\).
Complex multiplication
The elliptic curves in class 35280k do not have complex multiplication.Modular form 35280.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
