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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 58482.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58482.n1 | 58482j2 | \([1, -1, 0, -20103, 1202993]\) | \(-35937/4\) | \(-100008440178084\) | \([]\) | \(248832\) | \(1.4237\) | |
58482.n2 | 58482j1 | \([1, -1, 0, 1557, -2747]\) | \(109503/64\) | \(-243885847104\) | \([]\) | \(82944\) | \(0.87441\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58482.n have rank \(0\).
Complex multiplication
The elliptic curves in class 58482.n do not have complex multiplication.Modular form 58482.2.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.