Properties

Label 36414bk
Number of curves $1$
Conductor $36414$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 36414bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36414.i1 36414bk1 \([1, -1, 0, 736029, -291654027]\) \(30004847/42336\) \(-62219506853899061856\) \([]\) \(1175040\) \(2.4837\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 36414bk1 has rank \(1\).

Complex multiplication

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

Modular form 36414.2.a.bk

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} + q^{7} - q^{8} + 3 q^{10} + q^{11} + 4 q^{13} - q^{14} + q^{16} + O(q^{20})\) Copy content Toggle raw display