Properties

Label 18975.j
Number of curves $1$
Conductor $18975$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 18975.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18975.j1 18975j1 \([0, -1, 1, 15667, 411068]\) \(217732612096/164333367\) \(-320963607421875\) \([]\) \(48000\) \(1.4717\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 18975.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 18975.j do not have complex multiplication.

Modular form 18975.2.a.j

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