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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 23273b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23273.g4 | 23273b1 | \([1, -1, 0, -941, 4984]\) | \(35937/17\) | \(43617348953\) | \([2]\) | \(12960\) | \(0.73568\) | \(\Gamma_0(N)\)-optimal |
23273.g2 | 23273b2 | \([1, -1, 0, -7786, -259233]\) | \(20346417/289\) | \(741494932201\) | \([2, 2]\) | \(25920\) | \(1.0822\) | |
23273.g3 | 23273b3 | \([1, -1, 0, -941, -704158]\) | \(-35937/83521\) | \(-214292035406089\) | \([2]\) | \(51840\) | \(1.4288\) | |
23273.g1 | 23273b4 | \([1, -1, 0, -124151, -16806336]\) | \(82483294977/17\) | \(43617348953\) | \([2]\) | \(51840\) | \(1.4288\) |
Rank
sage: E.rank()
The elliptic curves in class 23273b have rank \(1\).
Complex multiplication
The elliptic curves in class 23273b do not have complex multiplication.Modular form 23273.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.