Properties

Label 19404.b
Number of curves $1$
Conductor $19404$
CM no
Rank $0$

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

Elliptic curves in class 19404.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19404.b1 19404v1 \([0, 0, 0, -10002909, 13392607529]\) \(-235165059164416/28529701497\) \(-13428487486802480255856\) \([]\) \(1182720\) \(2.9810\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19404.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 19404.b do not have complex multiplication.

Modular form 19404.2.a.b

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