Properties

Label 69696.gw
Number of curves $1$
Conductor $69696$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gw1")
 
E.isogeny_class()
 

Elliptic curves in class 69696.gw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69696.gw1 69696dn1 \([0, 0, 0, 132, -110]\) \(45056/27\) \(-152425152\) \([]\) \(23040\) \(0.25947\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 69696.gw1 has rank \(1\).

Complex multiplication

The elliptic curves in class 69696.gw do not have complex multiplication.

Modular form 69696.2.a.gw

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