Properties

Label 299538.x
Number of curves $1$
Conductor $299538$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 299538.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
299538.x1 299538x1 \([1, -1, 1, -347, 638627]\) \(-9/344\) \(-176138459997336\) \([]\) \(931392\) \(1.4124\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 299538.x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 299538.x do not have complex multiplication.

Modular form 299538.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 2 q^{7} + q^{8} + q^{10} - 4 q^{11} + 2 q^{14} + q^{16} + 3 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display