Properties

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

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Show commands: SageMath
E = EllipticCurve("ef1")
 
E.isogeny_class()
 

Elliptic curves in class 52416ef

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52416.eo1 52416ef1 \([0, 0, 0, 5268, 416848]\) \(2284322013/11927552\) \(-84421877170176\) \([]\) \(104448\) \(1.3544\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 52416ef1 has rank \(1\).

Complex multiplication

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

Modular form 52416.2.a.ef

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