Properties

Label 195994.g
Number of curves $1$
Conductor $195994$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 195994.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195994.g1 195994a1 \([1, 0, 0, -50886, 4416772]\) \(-2305199161/1696\) \(-10721031731104\) \([]\) \(792540\) \(1.4343\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 195994.g1 has rank \(0\).

Complex multiplication

The elliptic curves in class 195994.g do not have complex multiplication.

Modular form 195994.2.a.g

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