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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 152880.em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.em1 | 152880bu8 | \([0, 1, 0, -101920016, -396072412716]\) | \(242970740812818720001/24375\) | \(11746076160000\) | \([2]\) | \(9437184\) | \(2.8555\) | |
| 152880.em2 | 152880bu6 | \([0, 1, 0, -6370016, -6190192716]\) | \(59319456301170001/594140625\) | \(286310606400000000\) | \([2, 2]\) | \(4718592\) | \(2.5089\) | |
| 152880.em3 | 152880bu7 | \([0, 1, 0, -6217136, -6501272940]\) | \(-55150149867714721/5950927734375\) | \(-2867694375000000000000\) | \([2]\) | \(9437184\) | \(2.8555\) | |
| 152880.em4 | 152880bu4 | \([0, 1, 0, -407696, -91931820]\) | \(15551989015681/1445900625\) | \(696765491735040000\) | \([2, 2]\) | \(2359296\) | \(2.1624\) | |
| 152880.em5 | 152880bu2 | \([0, 1, 0, -90176, 8785524]\) | \(168288035761/27720225\) | \(13358107652198400\) | \([2, 2]\) | \(1179648\) | \(1.8158\) | |
| 152880.em6 | 152880bu1 | \([0, 1, 0, -86256, 9721620]\) | \(147281603041/5265\) | \(2537152450560\) | \([2]\) | \(589824\) | \(1.4692\) | \(\Gamma_0(N)\)-optimal |
| 152880.em7 | 152880bu3 | \([0, 1, 0, 164624, 49655444]\) | \(1023887723039/2798036865\) | \(-1348346835478056960\) | \([2]\) | \(2359296\) | \(2.1624\) | |
| 152880.em8 | 152880bu5 | \([0, 1, 0, 474304, -434500620]\) | \(24487529386319/183539412225\) | \(-88445863153086566400\) | \([2]\) | \(4718592\) | \(2.5089\) |
Rank
sage: E.rank()
The elliptic curves in class 152880.em have rank \(2\).
Complex multiplication
The elliptic curves in class 152880.em do not have complex multiplication.Modular form 152880.2.a.em
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
