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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 14994k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14994.f1 | 14994k1 | \([1, -1, 0, -8241, -286049]\) | \(-19486825371/11662\) | \(-37044611226\) | \([]\) | \(23040\) | \(0.97197\) | \(\Gamma_0(N)\)-optimal |
14994.f2 | 14994k2 | \([1, -1, 0, 7194, -1193284]\) | \(17779581/275128\) | \(-637109856139176\) | \([]\) | \(69120\) | \(1.5213\) |
Rank
sage: E.rank()
The elliptic curves in class 14994k have rank \(1\).
Complex multiplication
The elliptic curves in class 14994k do not have complex multiplication.Modular form 14994.2.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.