Properties

Label 1682.h
Number of curves $1$
Conductor $1682$
CM no
Rank $1$

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

Elliptic curves in class 1682.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1682.h1 1682j1 \([1, 1, 1, -39124, -2988683]\) \(13239457/32\) \(16007885214752\) \([]\) \(8700\) \(1.4125\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1682.h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1682.h do not have complex multiplication.

Modular form 1682.2.a.h

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