Properties

Label 137904bb
Number of curves $1$
Conductor $137904$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 137904bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137904.e1 137904bb1 \([0, -1, 0, -11717, -791571]\) \(-53248/51\) \(-170402884694016\) \([]\) \(474240\) \(1.4270\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 137904bb1 has rank \(1\).

Complex multiplication

The elliptic curves in class 137904bb do not have complex multiplication.

Modular form 137904.2.a.bb

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