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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 52983.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52983.a1 | 52983i2 | \([0, 0, 1, -16275873, 25276302306]\) | \(-1099616058781696/143578043\) | \(-62259201334396845387\) | \([]\) | \(6048000\) | \(2.8185\) | |
52983.a2 | 52983i1 | \([0, 0, 1, 148857, 762156]\) | \(841232384/487403\) | \(-211350711250389627\) | \([]\) | \(1209600\) | \(2.0138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52983.a have rank \(1\).
Complex multiplication
The elliptic curves in class 52983.a do not have complex multiplication.Modular form 52983.2.a.a
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.