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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 389205k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
389205.k2 | 389205k1 | \([0, 0, 1, -17298, -871387]\) | \(884736/5\) | \(3234950917245\) | \([]\) | \(736560\) | \(1.2424\) | \(\Gamma_0(N)\)-optimal |
389205.k1 | 389205k2 | \([0, 0, 1, -103788, 12266444]\) | \(2359296/125\) | \(6550775607421125\) | \([]\) | \(2209680\) | \(1.7917\) |
Rank
sage: E.rank()
The elliptic curves in class 389205k have rank \(0\).
Complex multiplication
The elliptic curves in class 389205k do not have complex multiplication.Modular form 389205.2.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.