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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 73920.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.n1 | 73920dz4 | \([0, -1, 0, -5709499521, -166050503697375]\) | \(78519570041710065450485106721/96428056919040\) | \(25278036552984821760\) | \([2]\) | \(35389440\) | \(3.8972\) | |
| 73920.n2 | 73920dz6 | \([0, -1, 0, -1679271041, 24243507729441]\) | \(1997773216431678333214187041/187585177195046990066400\) | \(49174328690618398163966361600\) | \([2]\) | \(70778880\) | \(4.2437\) | |
| 73920.n3 | 73920dz3 | \([0, -1, 0, -372903041, -2348135457759]\) | \(21876183941534093095979041/3572502915711058560000\) | \(936510204336159735152640000\) | \([2, 2]\) | \(35389440\) | \(3.8972\) | |
| 73920.n4 | 73920dz2 | \([0, -1, 0, -356846721, -2594404082655]\) | \(19170300594578891358373921/671785075055001600\) | \(176104426715218339430400\) | \([2, 2]\) | \(17694720\) | \(3.5506\) | |
| 73920.n5 | 73920dz1 | \([0, -1, 0, -21302401, -44334359519]\) | \(-4078208988807294650401/880065599546327040\) | \(-230703916527472355573760\) | \([2]\) | \(8847360\) | \(3.2040\) | \(\Gamma_0(N)\)-optimal |
| 73920.n6 | 73920dz5 | \([0, -1, 0, 676563839, -13178843552735]\) | \(130650216943167617311657439/361816948816603087500000\) | \(-94848142230579599769600000000\) | \([2]\) | \(70778880\) | \(4.2437\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.n have rank \(0\).
Complex multiplication
The elliptic curves in class 73920.n do not have complex multiplication.Modular form 73920.2.a.n
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.
