Properties

Label 41070d
Number of curves $1$
Conductor $41070$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 41070d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41070.g1 41070d1 \([1, 1, 0, -1184213, -496507707]\) \(-71581931663761/199800\) \(-512632136518200\) \([]\) \(590976\) \(2.0548\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41070d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 41070d do not have complex multiplication.

Modular form 41070.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 3 q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - q^{13} - 3 q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display