Properties

Label 40425cd
Number of curves $1$
Conductor $40425$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 40425cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40425.br1 40425cd1 \([0, 1, 1, 667217, -109222781]\) \(17869652393984/13156171875\) \(-24184538514404296875\) \([]\) \(903168\) \(2.4076\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40425cd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40425cd do not have complex multiplication.

Modular form 40425.2.a.cd

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