Properties

Label 747.d
Number of curves $1$
Conductor $747$
CM no
Rank $1$

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

Elliptic curves in class 747.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
747.d1 747d1 \([1, -1, 0, 9, 4]\) \(103823/83\) \(-60507\) \([]\) \(60\) \(-0.39456\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 747.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 747.d do not have complex multiplication.

Modular form 747.2.a.d

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