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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 8820.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8820.b1 | 8820s3 | \([0, 0, 0, -132888, -17221687]\) | \(189123395584/16078125\) | \(22063334627250000\) | \([2]\) | \(82944\) | \(1.8775\) | |
8820.b2 | 8820s1 | \([0, 0, 0, -27048, 1707797]\) | \(1594753024/4725\) | \(6483918747600\) | \([2]\) | \(27648\) | \(1.3282\) | \(\Gamma_0(N)\)-optimal |
8820.b3 | 8820s2 | \([0, 0, 0, -16023, 3112382]\) | \(-20720464/178605\) | \(-3921474058548480\) | \([2]\) | \(55296\) | \(1.6747\) | |
8820.b4 | 8820s4 | \([0, 0, 0, 142737, -79347562]\) | \(14647977776/132355125\) | \(-2906005930424352000\) | \([2]\) | \(165888\) | \(2.2240\) |
Rank
sage: E.rank()
The elliptic curves in class 8820.b have rank \(0\).
Complex multiplication
The elliptic curves in class 8820.b do not have complex multiplication.Modular form 8820.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.