Properties

Label 804.b
Number of curves $1$
Conductor $804$
CM no
Rank $1$

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

Elliptic curves in class 804.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
804.b1 804b1 \([0, -1, 0, -1373, -19191]\) \(-1118952448000/3956283\) \(-1012808448\) \([]\) \(360\) \(0.59025\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 804.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 804.b do not have complex multiplication.

Modular form 804.2.a.b

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