Properties

Label 463680gq
Number of curves $2$
Conductor $463680$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gq1")
 
E.isogeny_class()
 

Elliptic curves in class 463680gq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.gq1 463680gq1 \([0, 0, 0, -265548, 51337872]\) \(292583028222603/8456021875\) \(59850775756800000\) \([2]\) \(4423680\) \(1.9972\) \(\Gamma_0(N)\)-optimal
463680.gq2 463680gq2 \([0, 0, 0, 63732, 170273808]\) \(4044759171237/1771943359375\) \(-12541616640000000000\) \([2]\) \(8847360\) \(2.3437\)  

Rank

sage: E.rank()
 

The elliptic curves in class 463680gq have rank \(0\).

Complex multiplication

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

Modular form 463680.2.a.gq

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