Properties

Label 3920.ba
Number of curves $3$
Conductor $3920$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3920.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.ba1 3920bc3 \([0, 1, 0, -102965, -13337437]\) \(-250523582464/13671875\) \(-6588344000000000\) \([]\) \(20736\) \(1.7936\)  
3920.ba2 3920bc1 \([0, 1, 0, -1045, 14083]\) \(-262144/35\) \(-16866160640\) \([]\) \(2304\) \(0.69495\) \(\Gamma_0(N)\)-optimal
3920.ba3 3920bc2 \([0, 1, 0, 6795, -34525]\) \(71991296/42875\) \(-20661046784000\) \([]\) \(6912\) \(1.2443\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3920.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 3920.ba do not have complex multiplication.

Modular form 3920.2.a.ba

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

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.