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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 71050.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
71050.j1 | 71050n2 | \([1, 1, 0, -557400, 161030500]\) | \(-10418796526321/82044596\) | \(-150819760543812500\) | \([]\) | \(1008000\) | \(2.1248\) | |
71050.j2 | 71050n1 | \([1, 1, 0, 6100, -302000]\) | \(13651919/29696\) | \(-54589136000000\) | \([]\) | \(201600\) | \(1.3201\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 71050.j have rank \(0\).
Complex multiplication
The elliptic curves in class 71050.j do not have complex multiplication.Modular form 71050.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.