Properties

Label 43681.d
Number of curves $1$
Conductor $43681$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 43681.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43681.d1 43681b1 \([1, -1, 1, -30031, 1824364]\) \(9747\) \(307290101038811\) \([]\) \(142560\) \(1.5155\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 43681.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 43681.d do not have complex multiplication.

Modular form 43681.2.a.d

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