Properties

Label 363726k
Number of curves $1$
Conductor $363726$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 363726k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363726.k1 363726k1 \([1, -1, 0, -209655, 37000849]\) \(789145184521/22044\) \(28469119908636\) \([]\) \(1843200\) \(1.6841\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 363726k1 has rank \(2\).

Complex multiplication

The elliptic curves in class 363726k do not have complex multiplication.

Modular form 363726.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 3 q^{7} - q^{8} + q^{10} + q^{13} + 3 q^{14} + q^{16} - 4 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display