↑

Properties

Label 425880.co
Number of curves $4$
Conductor $425880$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 425880.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
425880.co1 425880co4 \([0, 0, 0, -2056416843, -35893420082858]\) \(266912903848829942596/152163375\) \(548274100668368256000\) \([2]\) \(115605504\) \(3.7404\)  
425880.co2 425880co2 \([0, 0, 0, -128549343, -560621263358]\) \(260798860029250384/196803140625\) \(177279954744172644000000\) \([2, 2]\) \(57802752\) \(3.3938\)  
425880.co3 425880co3 \([0, 0, 0, -101931843, -799449443858]\) \(-32506165579682596/57814914850875\) \(-208318331826444955280256000\) \([2]\) \(115605504\) \(3.7404\)  
425880.co4 425880co1 \([0, 0, 0, -9721218, -4814591483]\) \(1804588288006144/866455078125\) \(48781334405425781250000\) \([2]\) \(28901376\) \(3.0472\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 425880.co1.

Rank

sage: E.rank()
 

The elliptic curves in class 425880.co have rank \(0\).

Complex multiplication

The elliptic curves in class 425880.co do not have complex multiplication.

Modular form 425880.2.a.co

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + 4 q^{11} + 2 q^{17} + O(q^{20})\) Copy content 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 LMFDB 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 LMFDB labels.