Properties

Label 762.d
Number of curves $1$
Conductor $762$
CM no
Rank $1$

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

Elliptic curves in class 762.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
762.d1 762d1 \([1, 1, 1, -21, 27]\) \(1027243729/36576\) \(36576\) \([]\) \(80\) \(-0.35392\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 762.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 762.d do not have complex multiplication.

Modular form 762.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 3 q^{7} + q^{8} + q^{9} - q^{10} + q^{11} - q^{12} - 4 q^{13} - 3 q^{14} + q^{15} + q^{16} - 3 q^{17} + q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display