Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 299538.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
299538.h1 299538h1 \([1, -1, 0, -402504, -1116244738]\) \(-27/2\) \(-534196640560655561526\) \([]\) \(14303520\) \(2.6570\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 299538.h1 has rank \(1\).

Complex multiplication

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

Modular form 299538.2.a.h

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