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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 277200en
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.en1 | 277200en1 | \([0, 0, 0, -837675, 272828250]\) | \(51603494067/4336640\) | \(5462917447680000000\) | \([2]\) | \(4423680\) | \(2.3371\) | \(\Gamma_0(N)\)-optimal |
277200.en2 | 277200en2 | \([0, 0, 0, 890325, 1252604250]\) | \(61958108493/573927200\) | \(-722982980966400000000\) | \([2]\) | \(8847360\) | \(2.6837\) |
Rank
sage: E.rank()
The elliptic curves in class 277200en have rank \(1\).
Complex multiplication
The elliptic curves in class 277200en do not have complex multiplication.Modular form 277200.2.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.