Properties

Label 415794bg
Number of curves $1$
Conductor $415794$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 415794bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
415794.bg1 415794bg1 \([1, 1, 1, -455480, -117308551]\) \(70593496254289/824180736\) \(122008327950434304\) \([]\) \(6286896\) \(2.0909\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 415794bg1 has rank \(0\).

Complex multiplication

The elliptic curves in class 415794bg do not have complex multiplication.

Modular form 415794.2.a.bg

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