Properties

Label 9025.e
Number of curves $2$
Conductor $9025$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 9025.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9025.e1 9025d2 \([0, 1, 1, -7283, 175719]\) \(7575076864/1953125\) \(11016845703125\) \([]\) \(18144\) \(1.2118\)  
9025.e2 9025d1 \([0, 1, 1, -2533, -49906]\) \(318767104/125\) \(705078125\) \([]\) \(6048\) \(0.66249\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9025.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{4} + 4 q^{7} + q^{9} + 3 q^{11} + 4 q^{12} + 2 q^{13} + 4 q^{16} - 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.