Properties

Label 9025.d
Number of curves $3$
Conductor $9025$
CM no
Rank $0$
Graph

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

Elliptic curves in class 9025.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9025.d1 9025c3 \([0, 1, 1, -6943233, 7039600194]\) \(-50357871050752/19\) \(-13966745921875\) \([]\) \(116640\) \(2.3104\)  
9025.d2 9025c2 \([0, 1, 1, -84233, 9982569]\) \(-89915392/6859\) \(-5041995277796875\) \([]\) \(38880\) \(1.7611\)  
9025.d3 9025c1 \([0, 1, 1, 6017, 9944]\) \(32768/19\) \(-13966745921875\) \([]\) \(12960\) \(1.2118\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9025.d have rank \(0\).

Complex multiplication

The elliptic curves in class 9025.d do not have complex multiplication.

Modular form 9025.2.a.d

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.