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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1210.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1210.b1 | 1210g2 | \([1, 1, 0, -718742, 234235786]\) | \(-23178622194826561/1610510\) | \(-2853116706110\) | \([]\) | \(12000\) | \(1.8440\) | |
1210.b2 | 1210g1 | \([1, 1, 0, 1208, 65696]\) | \(109902239/1100000\) | \(-1948717100000\) | \([]\) | \(2400\) | \(1.0393\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1210.b have rank \(1\).
Complex multiplication
The elliptic curves in class 1210.b do not have complex multiplication.Modular form 1210.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.