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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 227430.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227430.j1 | 227430gf2 | \([1, -1, 0, -99205575, 379606831811]\) | \(17000365142097/38281250\) | \(243141902979545932031250\) | \([2]\) | \(37355520\) | \(3.3693\) | |
227430.j2 | 227430gf1 | \([1, -1, 0, -8461005, 1220123825]\) | \(10546683057/6002500\) | \(38124650387192802142500\) | \([2]\) | \(18677760\) | \(3.0228\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 227430.j have rank \(1\).
Complex multiplication
The elliptic curves in class 227430.j do not have complex multiplication.Modular form 227430.2.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.