Properties

Label 127756b
Number of curves $1$
Conductor $127756$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 127756b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127756.a1 127756b1 \([0, 1, 0, -35861, -2636057]\) \(-4194304/19\) \(-23104507028224\) \([]\) \(399360\) \(1.4159\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 127756b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 127756b do not have complex multiplication.

Modular form 127756.2.a.b

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