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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 6450.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6450.s1 | 6450n2 | \([1, 0, 1, -4144401, -3247777052]\) | \(503835593418244309249/898614000000\) | \(14040843750000000\) | \([2]\) | \(241920\) | \(2.3567\) | |
6450.s2 | 6450n1 | \([1, 0, 1, -256401, -51841052]\) | \(-119305480789133569/5200091136000\) | \(-81251424000000000\) | \([2]\) | \(120960\) | \(2.0101\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6450.s have rank \(1\).
Complex multiplication
The elliptic curves in class 6450.s do not have complex multiplication.Modular form 6450.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.