Properties

Label 242726h
Number of curves $1$
Conductor $242726$
CM no
Rank $1$

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

Elliptic curves in class 242726h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
242726.h1 242726h1 \([1, 1, 1, -10711, -431463]\) \(-76711450249/68204\) \(-120827546444\) \([]\) \(537600\) \(1.0515\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 242726h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 242726h do not have complex multiplication.

Modular form 242726.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 5 q^{7} + q^{8} - 2 q^{9} - q^{10} - q^{12} + 4 q^{13} + 5 q^{14} + q^{15} + q^{16} - q^{17} - 2 q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display