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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 338130.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.n1 | 338130n2 | \([1, -1, 0, -22887120, 21102681600]\) | \(2034416504287874043/882294347833600\) | \(575003898876875053996800\) | \([2]\) | \(50462720\) | \(3.2552\) | |
338130.n2 | 338130n1 | \([1, -1, 0, 4856880, 2442067200]\) | \(19441890357117957/15208161280000\) | \(-9911377140996464640000\) | \([2]\) | \(25231360\) | \(2.9087\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338130.n have rank \(1\).
Complex multiplication
The elliptic curves in class 338130.n do not have complex multiplication.Modular form 338130.2.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.