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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 215475.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215475.n1 | 215475q1 | \([1, 1, 1, -25637388, -48225860844]\) | \(89975616641/3581577\) | \(74181310646193791015625\) | \([2]\) | \(19768320\) | \(3.1550\) | \(\Gamma_0(N)\)-optimal |
215475.n2 | 215475q2 | \([1, 1, 1, 11436987, -176132454594]\) | \(7988005999/651714363\) | \(-13498251081657410935546875\) | \([2]\) | \(39536640\) | \(3.5016\) |
Rank
sage: E.rank()
The elliptic curves in class 215475.n have rank \(1\).
Complex multiplication
The elliptic curves in class 215475.n do not have complex multiplication.Modular form 215475.2.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.