Properties

Label 53824.d
Number of curves $1$
Conductor $53824$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 53824.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53824.d1 53824j1 \([0, 0, 0, -63916, 8975152]\) \(-185193/116\) \(-18087806300585984\) \([]\) \(645120\) \(1.8211\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53824.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 53824.d do not have complex multiplication.

Modular form 53824.2.a.d

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + 3 q^{5} - 2 q^{7} + 6 q^{9} - q^{11} - 3 q^{13} - 9 q^{15} + 4 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display