Properties

Label 57960bp
Number of curves $4$
Conductor $57960$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 57960bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57960.w4 57960bp1 \([0, 0, 0, -9183, 21922]\) \(458891455696/264449745\) \(49352669210880\) \([2]\) \(122880\) \(1.3171\) \(\Gamma_0(N)\)-optimal
57960.w2 57960bp2 \([0, 0, 0, -104403, 12952798]\) \(168591300897604/472410225\) \(352652343321600\) \([2, 2]\) \(245760\) \(1.6636\)  
57960.w3 57960bp3 \([0, 0, 0, -63003, 23327638]\) \(-18524646126002/146738831715\) \(-219079901839841280\) \([2]\) \(491520\) \(2.0102\)  
57960.w1 57960bp4 \([0, 0, 0, -1669323, 830154022]\) \(344577854816148242/2716875\) \(4056272640000\) \([2]\) \(491520\) \(2.0102\)  

Rank

sage: E.rank()
 

The elliptic curves in class 57960bp have rank \(1\).

Complex multiplication

The elliptic curves in class 57960bp do not have complex multiplication.

Modular form 57960.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + 4 q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.