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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 308550en
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.en2 | 308550en1 | \([1, 0, 1, -35158126, 79835999648]\) | \(173629978755828841/1000026931200\) | \(27681386097868800000000\) | \([2]\) | \(40550400\) | \(3.1474\) | \(\Gamma_0(N)\)-optimal |
308550.en1 | 308550en2 | \([1, 0, 1, -561750126, 5124587359648]\) | \(708234550511150304361/23696640000\) | \(655938175860000000000\) | \([2]\) | \(81100800\) | \(3.4940\) |
Rank
sage: E.rank()
The elliptic curves in class 308550en have rank \(1\).
Complex multiplication
The elliptic curves in class 308550en do not have complex multiplication.Modular form 308550.2.a.en
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 Cremona 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 Cremona labels.