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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 66270.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66270.x1 | 66270x2 | \([1, 0, 0, -1094603726, -13875795682044]\) | \(129602612829192047/680244480000\) | \(761282326727945724476160000\) | \([2]\) | \(38117376\) | \(4.0031\) | |
66270.x2 | 66270x1 | \([1, 0, 0, -31456206, -450156169980]\) | \(-3075827761007/76441190400\) | \(-85547665576890691013836800\) | \([2]\) | \(19058688\) | \(3.6566\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66270.x have rank \(0\).
Complex multiplication
The elliptic curves in class 66270.x do not have complex multiplication.Modular form 66270.2.a.x
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.