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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 73920cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73920.gh5 | 73920cv1 | \([0, 1, 0, -21302401, 44334359519]\) | \(-4078208988807294650401/880065599546327040\) | \(-230703916527472355573760\) | \([2]\) | \(8847360\) | \(3.2040\) | \(\Gamma_0(N)\)-optimal |
73920.gh4 | 73920cv2 | \([0, 1, 0, -356846721, 2594404082655]\) | \(19170300594578891358373921/671785075055001600\) | \(176104426715218339430400\) | \([2, 2]\) | \(17694720\) | \(3.5506\) | |
73920.gh3 | 73920cv3 | \([0, 1, 0, -372903041, 2348135457759]\) | \(21876183941534093095979041/3572502915711058560000\) | \(936510204336159735152640000\) | \([2, 2]\) | \(35389440\) | \(3.8972\) | |
73920.gh1 | 73920cv4 | \([0, 1, 0, -5709499521, 166050503697375]\) | \(78519570041710065450485106721/96428056919040\) | \(25278036552984821760\) | \([2]\) | \(35389440\) | \(3.8972\) | |
73920.gh6 | 73920cv5 | \([0, 1, 0, 676563839, 13178843552735]\) | \(130650216943167617311657439/361816948816603087500000\) | \(-94848142230579599769600000000\) | \([2]\) | \(70778880\) | \(4.2437\) | |
73920.gh2 | 73920cv6 | \([0, 1, 0, -1679271041, -24243507729441]\) | \(1997773216431678333214187041/187585177195046990066400\) | \(49174328690618398163966361600\) | \([2]\) | \(70778880\) | \(4.2437\) |
Rank
sage: E.rank()
The elliptic curves in class 73920cv have rank \(0\).
Complex multiplication
The elliptic curves in class 73920cv do not have complex multiplication.Modular form 73920.2.a.cv
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.