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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 29232.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29232.k1 | 29232bp4 | \([0, 0, 0, -168338186931, -26584107324268174]\) | \(176678690562294721133446471910833/3033870191363023488\) | \(9059087849486926326792192\) | \([2]\) | \(92897280\) | \(4.7831\) | |
| 29232.k2 | 29232bp3 | \([0, 0, 0, -11438183091, -338685241241230]\) | \(55425212630542527476751037873/15479334185118626660294016\) | \(46221044207417257309611367071744\) | \([2]\) | \(92897280\) | \(4.7831\) | |
| 29232.k3 | 29232bp2 | \([0, 0, 0, -10521467571, -415349243463310]\) | \(43138515777213631193352207793/5652352909513890349056\) | \(16877835350161924360035631104\) | \([2, 2]\) | \(46448640\) | \(4.4365\) | |
| 29232.k4 | 29232bp1 | \([0, 0, 0, -600627891, -7660273485454]\) | \(-8025141932308829504241073/3845373573888057802752\) | \(-11482223965652558390092627968\) | \([2]\) | \(23224320\) | \(4.0899\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29232.k have rank \(0\).
Complex multiplication
The elliptic curves in class 29232.k do not have complex multiplication.Modular form 29232.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
