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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 363726.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363726.r1 | 363726r2 | \([1, -1, 0, -937107, -348912437]\) | \(70470585447625/4518018\) | \(5834875530365442\) | \([2]\) | \(4423680\) | \(2.0829\) | |
363726.r2 | 363726r1 | \([1, -1, 0, -55017, -6132263]\) | \(-14260515625/4382748\) | \(-5660178658198812\) | \([2]\) | \(2211840\) | \(1.7363\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363726.r have rank \(0\).
Complex multiplication
The elliptic curves in class 363726.r do not have complex multiplication.Modular form 363726.2.a.r
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.