Properties

Label 417450.h
Number of curves $1$
Conductor $417450$
CM no
Rank $1$

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

Elliptic curves in class 417450.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
417450.h1 417450h1 \([1, 1, 0, -17896083075, 1042386147682125]\) \(-915970586489983193158705/148238892409964961792\) \(-102583687686207006905155200000000\) \([]\) \(2044224000\) \(4.8701\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 417450.h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 417450.h do not have complex multiplication.

Modular form 417450.2.a.h

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