Properties

Label 194271.j
Number of curves $1$
Conductor $194271$
CM no
Rank $0$

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

Elliptic curves in class 194271.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
194271.j1 194271f1 \([1, 0, 0, -1998654, -1088961153]\) \(-1484391946907017/1946200179\) \(-1157645253803574459\) \([]\) \(5040000\) \(2.3729\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 194271.j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 194271.j do not have complex multiplication.

Modular form 194271.2.a.j

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