Properties

Label 40425.x
Number of curves $1$
Conductor $40425$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 40425.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40425.x1 40425cv1 \([1, 0, 0, -5776513, 5343501092]\) \(-5916387959190625/288178803\) \(-1038308407320751875\) \([]\) \(1016064\) \(2.5294\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40425.x1 has rank \(1\).

Complex multiplication

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

Modular form 40425.2.a.x

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