Properties

Label 36414.p
Number of curves $1$
Conductor $36414$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 36414.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36414.p1 36414bb1 \([1, -1, 0, -236745, 44552389]\) \(-288568081/1176\) \(-5980344757199064\) \([]\) \(235008\) \(1.8834\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 36414.p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 36414.p do not have complex multiplication.

Modular form 36414.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 3 q^{11} + q^{14} + q^{16} + O(q^{20})\) Copy content Toggle raw display