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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 215600.fb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215600.fb1 | 215600ea2 | \([0, 1, 0, -116424408, -483558536812]\) | \(-23178622194826561/1610510\) | \(-12126393023360000000\) | \([]\) | \(19008000\) | \(3.1159\) | |
215600.fb2 | 215600ea1 | \([0, 1, 0, 195592, -134336812]\) | \(109902239/1100000\) | \(-8282489600000000000\) | \([]\) | \(3801600\) | \(2.3112\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215600.fb have rank \(1\).
Complex multiplication
The elliptic curves in class 215600.fb do not have complex multiplication.Modular form 215600.2.a.fb
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.