↑

Properties

Label 364650g
Number of curves $2$
Conductor $364650$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 364650g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.g1 364650g1 \([1, 1, 0, -164775, 26515125]\) \(-31665165722871409/1214021952000\) \(-18969093000000000\) \([]\) \(3359232\) \(1.8932\) \(\Gamma_0(N)\)-optimal
364650.g2 364650g2 \([1, 1, 0, 804225, 85318125]\) \(3681591091760239631/2330227453125000\) \(-36409803955078125000\) \([]\) \(10077696\) \(2.4425\)  

Rank

sage: E.rank()
 

The elliptic curves in class 364650g have rank \(1\).

Complex multiplication

The elliptic curves in class 364650g do not have complex multiplication.

Modular form 364650.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 2 q^{7} - q^{8} + q^{9} - q^{11} - q^{12} - q^{13} + 2 q^{14} + q^{16} - q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.