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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 357390.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 357390.q1 | 357390q3 | \([1, -1, 0, -76267635, 256383860741]\) | \(1430524893619449081/573412400\) | \(19666008128522487600\) | \([2]\) | \(35389440\) | \(3.0491\) | |
| 357390.q2 | 357390q2 | \([1, -1, 0, -4789635, 3966451541]\) | \(354308756121081/6988960000\) | \(239696497965371040000\) | \([2, 2]\) | \(17694720\) | \(2.7025\) | |
| 357390.q3 | 357390q1 | \([1, -1, 0, -630915, -99944875]\) | \(809818183161/342425600\) | \(11743981527107174400\) | \([2]\) | \(8847360\) | \(2.3559\) | \(\Gamma_0(N)\)-optimal |
| 357390.q4 | 357390q4 | \([1, -1, 0, 148845, 11748508325]\) | \(10633486599/1738618750000\) | \(-59628446245497318750000\) | \([2]\) | \(35389440\) | \(3.0491\) |
Rank
sage: E.rank()
The elliptic curves in class 357390.q have rank \(0\).
Complex multiplication
The elliptic curves in class 357390.q do not have complex multiplication.Modular form 357390.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
