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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 46800.ei
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.ei1 | 46800ci2 | \([0, 0, 0, -31677675, -34352875750]\) | \(2034416504287874043/882294347833600\) | \(1524604633056460800000000\) | \([2]\) | \(5898240\) | \(3.3365\) | |
46800.ei2 | 46800ci1 | \([0, 0, 0, 6722325, -3978475750]\) | \(19441890357117957/15208161280000\) | \(-26279702691840000000000\) | \([2]\) | \(2949120\) | \(2.9899\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.ei have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.ei do not have complex multiplication.Modular form 46800.2.a.ei
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.