Properties

Label 188760.cb
Number of curves $4$
Conductor $188760$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 188760.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.cb1 188760u3 \([0, 1, 0, -200416, 34336784]\) \(490757540836/2142075\) \(3885892125772800\) \([2]\) \(1966080\) \(1.8443\)  
188760.cb2 188760u2 \([0, 1, 0, -18916, -75616]\) \(1650587344/950625\) \(431127084960000\) \([2, 2]\) \(983040\) \(1.4977\)  
188760.cb3 188760u1 \([0, 1, 0, -13471, -604870]\) \(9538484224/26325\) \(746181493200\) \([2]\) \(491520\) \(1.1511\) \(\Gamma_0(N)\)-optimal
188760.cb4 188760u4 \([0, 1, 0, 75464, -528640]\) \(26198797244/15234375\) \(-27636351600000000\) \([2]\) \(1966080\) \(1.8443\)  

Rank

sage: E.rank()
 

The elliptic curves in class 188760.cb have rank \(0\).

Complex multiplication

The elliptic curves in class 188760.cb do not have complex multiplication.

Modular form 188760.2.a.cb

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4q^{7} + q^{9} - q^{13} - q^{15} + 6q^{17} + O(q^{20})\)  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 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.