Properties

Label 388311.b
Number of curves $1$
Conductor $388311$
CM no
Rank $2$

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

Elliptic curves in class 388311.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388311.b1 388311b1 \([0, 1, 1, 10264, -199786]\) \(71131770023936/51776124939\) \(-87035666022459\) \([]\) \(1236480\) \(1.3631\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388311.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 388311.b do not have complex multiplication.

Modular form 388311.2.a.b

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