Properties

Label 16184f
Number of curves $2$
Conductor $16184$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 16184f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16184.e1 16184f1 \([0, -1, 0, -232, 1212]\) \(275684/49\) \(246514688\) \([2]\) \(5120\) \(0.32965\) \(\Gamma_0(N)\)-optimal
16184.e2 16184f2 \([0, -1, 0, 448, 6380]\) \(986078/2401\) \(-24158439424\) \([2]\) \(10240\) \(0.67622\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16184f have rank \(1\).

Complex multiplication

The elliptic curves in class 16184f do not have complex multiplication.

Modular form 16184.2.a.f

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