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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 277350n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.n2 | 277350n1 | \([1, 1, 0, -10081234325, -391792543657875]\) | \(-9177493130077937309/59837484367872\) | \(-738778247320666374144000000000\) | \([2]\) | \(482549760\) | \(4.5676\) | \(\Gamma_0(N)\)-optimal |
277350.n1 | 277350n2 | \([1, 1, 0, -161551314325, -24992805586857875]\) | \(37767168555963845320349/1590072311808\) | \(19631688197463081216000000000\) | \([2]\) | \(965099520\) | \(4.9141\) |
Rank
sage: E.rank()
The elliptic curves in class 277350n have rank \(1\).
Complex multiplication
The elliptic curves in class 277350n do not have complex multiplication.Modular form 277350.2.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 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.