Properties

Label 47040z
Number of curves $1$
Conductor $47040$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 47040z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47040.ca1 47040z1 \([0, -1, 0, -65, 14337]\) \(-392/1125\) \(-88510464000\) \([]\) \(50688\) \(0.77948\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47040z1 has rank \(2\).

Complex multiplication

The elliptic curves in class 47040z do not have complex multiplication.

Modular form 47040.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 5 q^{11} - q^{13} - q^{15} - 8 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display