Properties

Label 17640.a
Number of curves $2$
Conductor $17640$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 17640.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17640.a1 17640g2 \([0, 0, 0, -213003, -37210698]\) \(1314036/25\) \(20333569192473600\) \([2]\) \(172032\) \(1.9226\)  
17640.a2 17640g1 \([0, 0, 0, -27783, 907578]\) \(11664/5\) \(1016678459623680\) \([2]\) \(86016\) \(1.5761\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17640.a have rank \(0\).

Complex multiplication

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

Modular form 17640.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.