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Properties

Label 9405.j
Number of curves $2$
Conductor $9405$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 9405.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9405.j1 9405m2 \([1, -1, 0, -279, -1620]\) \(3301293169/218405\) \(159217245\) \([2]\) \(3072\) \(0.32326\)  
9405.j2 9405m1 \([1, -1, 0, -54, 135]\) \(24137569/5225\) \(3809025\) \([2]\) \(1536\) \(-0.023311\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9405.j have rank \(0\).

Complex multiplication

The elliptic curves in class 9405.j do not have complex multiplication.

Modular form 9405.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} + q^{11} + 6 q^{13} - 2 q^{14} - q^{16} - q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.