Properties

Label 1850.h
Number of curves $1$
Conductor $1850$
CM no
Rank $1$

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

Elliptic curves in class 1850.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.h1 1850m1 \([1, -1, 1, -3105, 72177]\) \(-132384574175625/11484004352\) \(-287100108800\) \([]\) \(4416\) \(0.94288\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1850.h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1850.h do not have complex multiplication.

Modular form 1850.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} - 3 q^{6} + q^{8} + 6 q^{9} - q^{11} - 3 q^{12} - 2 q^{13} + q^{16} - 7 q^{17} + 6 q^{18} + 5 q^{19} + O(q^{20})\)  Toggle raw display