Properties

Label 19008.r
Number of curves $1$
Conductor $19008$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 19008.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19008.r1 19008k1 \([0, 0, 0, -36, -86]\) \(-2985984/121\) \(-209088\) \([]\) \(1920\) \(-0.21128\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19008.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 19008.r do not have complex multiplication.

Modular form 19008.2.a.r

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