Properties

Label 192987.d
Number of curves $1$
Conductor $192987$
CM no
Rank $1$

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

Elliptic curves in class 192987.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
192987.d1 192987d1 \([1, -1, 0, -45, -212]\) \(-13997521/21443\) \(-15631947\) \([]\) \(87360\) \(0.071923\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 192987.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 192987.d do not have complex multiplication.

Modular form 192987.2.a.d

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