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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5610.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.b1 | 5610d2 | \([1, 1, 0, -143, 363]\) | \(326940373369/112003650\) | \(112003650\) | \([2]\) | \(2048\) | \(0.24646\) | |
5610.b2 | 5610d1 | \([1, 1, 0, 27, 57]\) | \(2053225511/2098140\) | \(-2098140\) | \([2]\) | \(1024\) | \(-0.10012\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5610.b have rank \(1\).
Complex multiplication
The elliptic curves in class 5610.b do not have complex multiplication.Modular form 5610.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.