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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 5950.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5950.k1 | 5950n2 | \([1, 0, 0, -3213, -13583]\) | \(234770924809/130960928\) | \(2046264500000\) | \([2]\) | \(12800\) | \(1.0526\) | |
5950.k2 | 5950n1 | \([1, 0, 0, 787, -1583]\) | \(3449795831/2071552\) | \(-32368000000\) | \([2]\) | \(6400\) | \(0.70598\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5950.k have rank \(1\).
Complex multiplication
The elliptic curves in class 5950.k do not have complex multiplication.Modular form 5950.2.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 LMFDB 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 LMFDB labels.