Properties

Label 9633m
Number of curves $4$
Conductor $9633$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 9633m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9633.h3 9633m1 \([1, 0, 0, -257, -1392]\) \(389017/57\) \(275128113\) \([2]\) \(2880\) \(0.34432\) \(\Gamma_0(N)\)-optimal
9633.h2 9633m2 \([1, 0, 0, -1102, 12635]\) \(30664297/3249\) \(15682302441\) \([2, 2]\) \(5760\) \(0.69089\)  
9633.h1 9633m3 \([1, 0, 0, -17157, 863550]\) \(115714886617/1539\) \(7428459051\) \([2]\) \(11520\) \(1.0375\)  
9633.h4 9633m4 \([1, 0, 0, 1433, 62828]\) \(67419143/390963\) \(-1887103727067\) \([2]\) \(11520\) \(1.0375\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9633m have rank \(1\).

Complex multiplication

The elliptic curves in class 9633m do not have complex multiplication.

Modular form 9633.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + q^{9} - 2 q^{10} - q^{12} + 2 q^{15} - q^{16} - 6 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.