Properties

Label 21904b
Number of curves $1$
Conductor $21904$
CM no
Rank $1$

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

Elliptic curves in class 21904b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21904.j1 21904b1 \([0, 1, 0, -12777, -507037]\) \(351232/37\) \(24302560546048\) \([]\) \(43776\) \(1.3032\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21904b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 21904b do not have complex multiplication.

Modular form 21904.2.a.b

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