Properties

Label 19600.cp
Number of curves $1$
Conductor $19600$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 19600.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.cp1 19600k1 \([0, 1, 0, 262967, 162866563]\) \(12459008/78125\) \(-12610502187500000000\) \([]\) \(301056\) \(2.3469\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19600.cp1 has rank \(0\).

Complex multiplication

The elliptic curves in class 19600.cp do not have complex multiplication.

Modular form 19600.2.a.cp

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