Properties

Label 3549.d
Number of curves $1$
Conductor $3549$
CM no
Rank $1$

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

Elliptic curves in class 3549.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3549.d1 3549a1 \([0, -1, 1, -4450, 132225]\) \(-2019487744/361179\) \(-1743342047811\) \([]\) \(8064\) \(1.0743\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3549.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3549.d do not have complex multiplication.

Modular form 3549.2.a.d

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