Properties

Label 88935.q
Number of curves $4$
Conductor $88935$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 88935.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.q1 88935bi4 \([1, 1, 1, -12175325, -16357000318]\) \(957681397954009/31185\) \(6499651923075465\) \([2]\) \(2211840\) \(2.5355\)  
88935.q2 88935bi3 \([1, 1, 1, -1206675, 76290402]\) \(932288503609/527295615\) \(109900207088793009735\) \([2]\) \(2211840\) \(2.5355\)  
88935.q3 88935bi2 \([1, 1, 1, -762000, -255081408]\) \(234770924809/1334025\) \(278040665598228225\) \([2, 2]\) \(1105920\) \(2.1889\)  
88935.q4 88935bi1 \([1, 1, 1, -20875, -8435008]\) \(-4826809/144375\) \(-30090981125349375\) \([4]\) \(552960\) \(1.8423\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 88935.q have rank \(0\).

Complex multiplication

The elliptic curves in class 88935.q do not have complex multiplication.

Modular form 88935.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3 q^{8} + q^{9} - q^{10} + q^{12} - 2 q^{13} - q^{15} - q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.