Properties

Label 16762.d
Number of curves $1$
Conductor $16762$
CM no
Rank $0$

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

Elliptic curves in class 16762.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16762.d1 16762d1 \([1, -1, 0, -343, 3617]\) \(-185193/116\) \(-2799958004\) \([]\) \(19712\) \(0.51438\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 16762.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 16762.d do not have complex multiplication.

Modular form 16762.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} + 2 q^{7} - q^{8} + 6 q^{9} - 3 q^{10} + q^{11} + 3 q^{12} + 3 q^{13} - 2 q^{14} + 9 q^{15} + q^{16} - 6 q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display