Properties

Label 299538r
Number of curves $1$
Conductor $299538$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 299538r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
299538.r1 299538r1 \([1, -1, 1, -44723, 41357305]\) \(-27/2\) \(-732780028203917094\) \([]\) \(4767840\) \(2.1077\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 299538r1 has rank \(1\).

Complex multiplication

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

Modular form 299538.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{10} - 6 q^{11} + 2 q^{13} - 2 q^{14} + q^{16} - 7 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display