Properties

Label 39039.p
Number of curves $1$
Conductor $39039$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 39039.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.p1 39039t1 \([0, 1, 1, -5540045, 5018901008]\) \(-3895861901277528064/1561102682139\) \(-7535144476072664451\) \([]\) \(940800\) \(2.5858\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 39039.p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 39039.p do not have complex multiplication.

Modular form 39039.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{5} - q^{7} + q^{9} + q^{11} - 2 q^{12} + q^{15} + 4 q^{16} - 4 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display