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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 6498.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6498.s1 | 6498s2 | \([1, -1, 1, -302225, 64140545]\) | \(-246579625/512\) | \(-6339080937927168\) | \([3]\) | \(61560\) | \(1.9179\) | |
6498.s2 | 6498s1 | \([1, -1, 1, 6430, 434153]\) | \(2375/8\) | \(-99048139655112\) | \([]\) | \(20520\) | \(1.3686\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6498.s have rank \(1\).
Complex multiplication
The elliptic curves in class 6498.s do not have complex multiplication.Modular form 6498.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.