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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 236992.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236992.j1 | 236992j2 | \([0, 1, 0, -474689, 105620767]\) | \(304821217/51842\) | \(2011817982699241472\) | \([2]\) | \(4866048\) | \(2.2328\) | |
236992.j2 | 236992j1 | \([0, 1, 0, -136129, -17818209]\) | \(7189057/644\) | \(24991527735394304\) | \([2]\) | \(2433024\) | \(1.8862\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.j have rank \(0\).
Complex multiplication
The elliptic curves in class 236992.j do not have complex multiplication.Modular form 236992.2.a.j
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.