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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5850.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5850.i1 | 5850a2 | \([1, -1, 0, -245742, -46827334]\) | \(-8538302475/26\) | \(-4997636718750\) | \([]\) | \(38880\) | \(1.6639\) | |
5850.i2 | 5850a1 | \([1, -1, 0, -1992, -108584]\) | \(-3316275/17576\) | \(-4634296875000\) | \([]\) | \(12960\) | \(1.1146\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5850.i have rank \(1\).
Complex multiplication
The elliptic curves in class 5850.i do not have complex multiplication.Modular form 5850.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.