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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 215475k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215475.u1 | 215475k1 | \([1, 0, 0, -6068, -176073]\) | \(89975616641/3581577\) | \(983590583625\) | \([2]\) | \(304128\) | \(1.0678\) | \(\Gamma_0(N)\)-optimal |
215475.u2 | 215475k2 | \([1, 0, 0, 2707, -641148]\) | \(7988005999/651714363\) | \(-178977056938875\) | \([2]\) | \(608256\) | \(1.4144\) |
Rank
sage: E.rank()
The elliptic curves in class 215475k have rank \(1\).
Complex multiplication
The elliptic curves in class 215475k do not have complex multiplication.Modular form 215475.2.a.k
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.