Properties

Label 36414y
Number of curves $1$
Conductor $36414$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 36414y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36414.b1 36414y1 \([1, -1, 0, -10764, 432544]\) \(654699641761/112\) \(23596272\) \([]\) \(60480\) \(0.81334\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 36414y1 has rank \(2\).

Complex multiplication

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

Modular form 36414.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 4 q^{5} - q^{7} - q^{8} + 4 q^{10} - 2 q^{13} + q^{14} + q^{16} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display