Properties

Label 487872ni
Number of curves $4$
Conductor $487872$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ni1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 487872ni

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
487872.ni3 487872ni1 \([0, 0, 0, -2556851484, 49762978590512]\) \(87364831012240243408/1760913\) \(37259882261638299648\) \([2]\) \(176947200\) \(3.7388\) \(\Gamma_0(N)\)-optimal
487872.ni2 487872ni2 \([0, 0, 0, -2556938604, 49759417856720]\) \(21843440425782779332/3100814593569\) \(262445644211953132592234496\) \([2, 2]\) \(353894400\) \(4.0854\)  
487872.ni4 487872ni3 \([0, 0, 0, -2326419084, 59095919455760]\) \(-8226100326647904626/4152140742401883\) \(-702854826766095092257341702144\) \([2]\) \(707788800\) \(4.4320\)  
487872.ni1 487872ni4 \([0, 0, 0, -2788852044, 40195029294992]\) \(14171198121996897746/4077720290568771\) \(690257283227443598222439088128\) \([2]\) \(707788800\) \(4.4320\)  

Rank

sage: E.rank()
 

The elliptic curves in class 487872ni have rank \(1\).

Complex multiplication

The elliptic curves in class 487872ni do not have complex multiplication.

Modular form 487872.2.a.ni

sage: E.q_eigenform(10)
 
\(q + 2q^{5} + q^{7} - 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.