Properties

Label 52416ce
Number of curves $1$
Conductor $52416$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 52416ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52416.fz1 52416ce1 \([0, 0, 0, -57878796, 170452995568]\) \(-112205650221491190337/745029571313664\) \(-142377368286045419864064\) \([]\) \(7311360\) \(3.2783\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 52416ce1 has rank \(1\).

Complex multiplication

The elliptic curves in class 52416ce do not have complex multiplication.

Modular form 52416.2.a.ce

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