Properties

Label 3200.f
Number of curves $2$
Conductor $3200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 3200.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3200.f1 3200h1 \([0, 1, 0, -1658, 25438]\) \(252179168/25\) \(50000000\) \([2]\) \(1536\) \(0.51201\) \(\Gamma_0(N)\)-optimal
3200.f2 3200h2 \([0, 1, 0, -1533, 29563]\) \(-1557376/625\) \(-160000000000\) \([2]\) \(3072\) \(0.85858\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3200.f have rank \(1\).

Complex multiplication

The elliptic curves in class 3200.f do not have complex multiplication.

Modular form 3200.2.a.f

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