↑

Properties

Label 9438m
Number of curves $2$
Conductor $9438$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 9438m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9438.m1 9438m1 \([1, 0, 1, -698702524, -7116255551110]\) \(-21293376668673906679951249/26211168887701209984\) \(-46434684565864843260465024\) \([]\) \(4233600\) \(3.8348\) \(\Gamma_0(N)\)-optimal
9438.m2 9438m2 \([1, 0, 1, 1978723766, 446609728005890]\) \(483641001192506212470106511/48918776756543177755473774\) \(-86662597069598388527664874541214\) \([]\) \(29635200\) \(4.8077\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9438m have rank \(0\).

Complex multiplication

The elliptic curves in class 9438m do not have complex multiplication.

Modular form 9438.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + q^{13} + q^{14} - q^{15} + q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.