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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 141120.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.k1 | 141120cv1 | \([0, 0, 0, -615468, -105986608]\) | \(393349474783/153600000\) | \(10068222069964800000\) | \([2]\) | \(3440640\) | \(2.3450\) | \(\Gamma_0(N)\)-optimal |
141120.k2 | 141120cv2 | \([0, 0, 0, 1965012, -763492912]\) | \(12801408679457/11250000000\) | \(-737418608640000000000\) | \([2]\) | \(6881280\) | \(2.6916\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.k have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.k do not have complex multiplication.Modular form 141120.2.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.