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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 54150.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.k1 | 54150c2 | \([1, 1, 0, -644525, 198868125]\) | \(276288773643091/41990400\) | \(4500189900000000\) | \([2]\) | \(491520\) | \(2.0161\) | |
54150.k2 | 54150c1 | \([1, 1, 0, -36525, 3700125]\) | \(-50284268371/26542080\) | \(-2844564480000000\) | \([2]\) | \(245760\) | \(1.6695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.k have rank \(1\).
Complex multiplication
The elliptic curves in class 54150.k do not have complex multiplication.Modular form 54150.2.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.