Properties

Label 463680gp
Number of curves $2$
Conductor $463680$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("gp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 463680gp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.gp1 463680gp1 \([0, 0, 0, -348, -688]\) \(10536048/5635\) \(2492743680\) \([2]\) \(245760\) \(0.49432\) \(\Gamma_0(N)\)-optimal
463680.gp2 463680gp2 \([0, 0, 0, 1332, -5392]\) \(147704148/92575\) \(-163808870400\) \([2]\) \(491520\) \(0.84089\)  

Rank

sage: E.rank()
 

The elliptic curves in class 463680gp have rank \(1\).

Complex multiplication

The elliptic curves in class 463680gp do not have complex multiplication.

Modular form 463680.2.a.gp

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