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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 210210.ey
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
210210.ey1 | 210210s2 | \([1, 0, 0, -1436975, 662892957]\) | \(2789222297765780449/677605500\) | \(79719609469500\) | \([2]\) | \(3317760\) | \(2.0447\) | |
210210.ey2 | 210210s1 | \([1, 0, 0, -89475, 10433457]\) | \(-673350049820449/10617750000\) | \(-1249167669750000\) | \([2]\) | \(1658880\) | \(1.6981\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 210210.ey have rank \(1\).
Complex multiplication
The elliptic curves in class 210210.ey do not have complex multiplication.Modular form 210210.2.a.ey
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.