Properties

Label 49686bl
Number of curves $1$
Conductor $49686$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 49686bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.bp1 49686bl1 \([1, 0, 1, -832108177, 9291628742372]\) \(-112205650221491190337/745029571313664\) \(-423079385410317245483188224\) \([]\) \(38384640\) \(3.9447\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 49686bl1 has rank \(1\).

Complex multiplication

The elliptic curves in class 49686bl do not have complex multiplication.

Modular form 49686.2.a.bl

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