Properties

Label 9075.j
Number of curves $2$
Conductor $9075$
CM no
Rank $0$
Graph

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

Elliptic curves in class 9075.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9075.j1 9075g2 \([0, -1, 1, -149783, 22362218]\) \(-196566176333824/421875\) \(-797607421875\) \([]\) \(31104\) \(1.5312\)  
9075.j2 9075g1 \([0, -1, 1, -1283, 50093]\) \(-123633664/492075\) \(-930329296875\) \([]\) \(10368\) \(0.98194\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9075.j have rank \(0\).

Complex multiplication

The elliptic curves in class 9075.j do not have complex multiplication.

Modular form 9075.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.