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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 141570.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.j1 | 141570ew2 | \([1, -1, 0, -86242470, 154338972596]\) | \(2034416504287874043/882294347833600\) | \(30765282015334651432876800\) | \([2]\) | \(39321600\) | \(3.5869\) | |
141570.j2 | 141570ew1 | \([1, -1, 0, 18301530, 17867234996]\) | \(19441890357117957/15208161280000\) | \(-530303035333663088640000\) | \([2]\) | \(19660800\) | \(3.2403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141570.j have rank \(1\).
Complex multiplication
The elliptic curves in class 141570.j do not have complex multiplication.Modular form 141570.2.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.