Properties

Label 9405.d
Number of curves $4$
Conductor $9405$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 9405.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9405.d1 9405i3 \([1, -1, 1, -9151103, 9375314212]\) \(116256292809537371612841/15216540068579856875\) \(11092857709994715661875\) \([2]\) \(565248\) \(2.9583\)  
9405.d2 9405i2 \([1, -1, 1, -8841728, 10121402962]\) \(104859453317683374662841/2223652969140625\) \(1621043014503515625\) \([2, 2]\) \(282624\) \(2.6117\)  
9405.d3 9405i1 \([1, -1, 1, -8841683, 10121511106]\) \(104857852278310619039721/47155625\) \(34376450625\) \([2]\) \(141312\) \(2.2651\) \(\Gamma_0(N)\)-optimal
9405.d4 9405i4 \([1, -1, 1, -8533073, 10860569956]\) \(-94256762600623910012361/15323275604248046875\) \(-11170667915496826171875\) \([2]\) \(565248\) \(2.9583\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9405.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 3 q^{8} + q^{10} + q^{11} + 2 q^{13} - q^{16} + 6 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.