Properties

Label 190463bt
Number of curves $1$
Conductor $190463$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 190463bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190463.bt1 190463bt1 \([0, 0, 1, -12678211, 24349197759]\) \(-396870925750272/221358574619\) \(-125702728201753416547379\) \([]\) \(59996160\) \(3.1357\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 190463bt1 has rank \(1\).

Complex multiplication

The elliptic curves in class 190463bt do not have complex multiplication.

Modular form 190463.2.a.bt

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