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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 57960.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57960.n1 | 57960a1 | \([0, 0, 0, -83943, 9361018]\) | \(9463971881004912/44454515\) | \(307269607680\) | \([2]\) | \(179200\) | \(1.4065\) | \(\Gamma_0(N)\)-optimal |
57960.n2 | 57960a2 | \([0, 0, 0, -82563, 9683662]\) | \(-2251211955310188/162423268175\) | \(-4490678518502400\) | \([2]\) | \(358400\) | \(1.7531\) |
Rank
sage: E.rank()
The elliptic curves in class 57960.n have rank \(0\).
Complex multiplication
The elliptic curves in class 57960.n do not have complex multiplication.Modular form 57960.2.a.n
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.