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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 5776.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5776.n1 | 5776m2 | \([0, 1, 0, -1488, -22636]\) | \(-246579625/512\) | \(-757071872\) | \([]\) | \(2592\) | \(0.58955\) | |
5776.n2 | 5776m1 | \([0, 1, 0, 32, -140]\) | \(2375/8\) | \(-11829248\) | \([]\) | \(864\) | \(0.040246\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5776.n have rank \(1\).
Complex multiplication
The elliptic curves in class 5776.n do not have complex multiplication.Modular form 5776.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.