Properties

Label 1617.h
Number of curves $1$
Conductor $1617$
CM no
Rank $1$

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

Elliptic curves in class 1617.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1617.h1 1617e1 \([1, 0, 1, -1251, 17539]\) \(-765625/33\) \(-9321683217\) \([]\) \(1008\) \(0.67878\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1617.h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1617.h do not have complex multiplication.

Modular form 1617.2.a.h

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