Properties

Label 47040hj
Number of curves $1$
Conductor $47040$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("hj1")
 
E.isogeny_class()
 

Elliptic curves in class 47040hj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47040.fr1 47040hj1 \([0, 1, 0, -9376705, 12710246975]\) \(-1231272543361/230400000\) \(-17060933761656422400000\) \([]\) \(4193280\) \(2.9902\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47040hj1 has rank \(1\).

Complex multiplication

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

Modular form 47040.2.a.hj

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