Properties

Label 450840p
Number of curves $4$
Conductor $450840$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 450840p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.p3 450840p1 \([0, -1, 0, -9055911, 10492288740]\) \(212670222886967296/616241925\) \(237993311766085200\) \([2]\) \(14155776\) \(2.5643\) \(\Gamma_0(N)\)-optimal
450840.p2 450840p2 \([0, -1, 0, -9172956, 10207260756]\) \(13813960087661776/714574355625\) \(4415510480519417760000\) \([2, 2]\) \(28311552\) \(2.9109\)  
450840.p4 450840p3 \([0, -1, 0, 5860824, 40377050460]\) \(900753985478876/29018422265625\) \(-717244589780643600000000\) \([2]\) \(56623104\) \(3.2575\)  
450840.p1 450840p4 \([0, -1, 0, -26079456, -38206192644]\) \(79364416584061444/20404090514925\) \(504325266110717662540800\) \([2]\) \(56623104\) \(3.2575\)  

Rank

sage: E.rank()
 

The elliptic curves in class 450840p have rank \(0\).

Complex multiplication

The elliptic curves in class 450840p do not have complex multiplication.

Modular form 450840.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 4q^{7} + q^{9} + q^{13} + q^{15} + O(q^{20})\)  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.