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SageMath
E = EllipticCurve("mo1")
E.isogeny_class()
Elliptic curves in class 242550.mo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.mo1 | 242550mo3 | \([1, -1, 1, -983550503480, 375442467559113147]\) | \(78519570041710065450485106721/96428056919040\) | \(129222818711144872560000000\) | \([2]\) | \(1698693120\) | \(5.1844\) | |
| 242550.mo2 | 242550mo6 | \([1, -1, 1, -289280675480, -54812901598934853]\) | \(1997773216431678333214187041/187585177195046990066400\) | \(251382078204950636730010319287500000\) | \([2]\) | \(3397386240\) | \(5.5310\) | |
| 242550.mo3 | 242550mo4 | \([1, -1, 1, -64238375480, 5309399269065147]\) | \(21876183941534093095979041/3572502915711058560000\) | \(4787495583464491398360090000000000\) | \([2, 2]\) | \(1698693120\) | \(5.1844\) | |
| 242550.mo4 | 242550mo2 | \([1, -1, 1, -61472423480, 5866196470473147]\) | \(19170300594578891358373921/671785075055001600\) | \(900256250518146076262400000000\) | \([2, 2]\) | \(849346560\) | \(4.8378\) | |
| 242550.mo5 | 242550mo1 | \([1, -1, 1, -3669671480, 100256352969147]\) | \(-4078208988807294650401/880065599546327040\) | \(-1179372073416059844034560000000\) | \([2]\) | \(424673280\) | \(4.4913\) | \(\Gamma_0(N)\)-optimal |
| 242550.mo6 | 242550mo5 | \([1, -1, 1, 116548692520, 29796646055529147]\) | \(130650216943167617311657439/361816948816603087500000\) | \(-484869315813368550179665429687500000\) | \([2]\) | \(3397386240\) | \(5.5310\) |
Rank
sage: E.rank()
The elliptic curves in class 242550.mo have rank \(1\).
Complex multiplication
The elliptic curves in class 242550.mo do not have complex multiplication.Modular form 242550.2.a.mo
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
