Properties

Label 67830s
Number of curves $1$
Conductor $67830$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 67830s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67830.p1 67830s1 \([1, 0, 1, 86849626, 4484452919672]\) \(72448196218150707243102543911/8729555368583338109588880000\) \(-8729555368583338109588880000\) \([]\) \(64995840\) \(4.0407\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67830s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 67830s do not have complex multiplication.

Modular form 67830.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 6 q^{11} + q^{12} - q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display