Properties

Label 38640.cf
Number of curves $4$
Conductor $38640$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("cf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38640.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.cf1 38640cn4 \([0, 1, 0, -71856, 7389780]\) \(10017490085065009/235066440\) \(962832138240\) \([2]\) \(147456\) \(1.4114\)  
38640.cf2 38640cn3 \([0, 1, 0, -19376, -936876]\) \(196416765680689/22365315000\) \(91608330240000\) \([2]\) \(147456\) \(1.4114\)  
38640.cf3 38640cn2 \([0, 1, 0, -4656, 105300]\) \(2725812332209/373262400\) \(1528882790400\) \([2, 2]\) \(73728\) \(1.0649\)  
38640.cf4 38640cn1 \([0, 1, 0, 464, 9044]\) \(2691419471/9891840\) \(-40516976640\) \([2]\) \(36864\) \(0.71829\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38640.cf have rank \(0\).

Complex multiplication

The elliptic curves in class 38640.cf do not have complex multiplication.

Modular form 38640.2.a.cf

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} + 6q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.