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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 28611.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28611.j1 | 28611y1 | \([0, 0, 1, -4804914, -4055341275]\) | \(-2412468600832/970299\) | \(-4934287872079502211\) | \([]\) | \(822528\) | \(2.5503\) | \(\Gamma_0(N)\)-optimal |
28611.j2 | 28611y2 | \([0, 0, 1, 3154146, -15657660990]\) | \(682417553408/21221529219\) | \(-107918419221593024894091\) | \([3]\) | \(2467584\) | \(3.0997\) |
Rank
sage: E.rank()
The elliptic curves in class 28611.j have rank \(0\).
Complex multiplication
The elliptic curves in class 28611.j do not have complex multiplication.Modular form 28611.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.