Properties

Label 9075.f
Number of curves $2$
Conductor $9075$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9075.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9075.f1 9075s2 \([1, 0, 0, -856138, -303556483]\) \(15069223/81\) \(373034693302734375\) \([2]\) \(168960\) \(2.2158\)  
9075.f2 9075s1 \([1, 0, 0, -24263, -9904608]\) \(-343/9\) \(-41448299255859375\) \([2]\) \(84480\) \(1.8692\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9075.f have rank \(1\).

Complex multiplication

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

Modular form 9075.2.a.f

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