Properties

Label 17640t
Number of curves $4$
Conductor $17640$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 17640t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17640.bg3 17640t1 \([0, 0, 0, -31458, -2058343]\) \(2508888064/118125\) \(162097968690000\) \([2]\) \(73728\) \(1.4874\) \(\Gamma_0(N)\)-optimal
17640.bg2 17640t2 \([0, 0, 0, -86583, 7125482]\) \(3269383504/893025\) \(19607370292742400\) \([2, 2]\) \(147456\) \(1.8340\)  
17640.bg1 17640t3 \([0, 0, 0, -1277283, 555561902]\) \(2624033547076/324135\) \(28466996869463040\) \([2]\) \(294912\) \(2.1805\)  
17640.bg4 17640t4 \([0, 0, 0, 222117, 46453862]\) \(13799183324/18600435\) \(-1633574050675338240\) \([2]\) \(294912\) \(2.1805\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17640t have rank \(1\).

Complex multiplication

The elliptic curves in class 17640t do not have complex multiplication.

Modular form 17640.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{11} + 6 q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})\) 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 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.