Properties

Label 191100.cp
Number of curves $1$
Conductor $191100$
CM no
Rank $1$

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

Elliptic curves in class 191100.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
191100.cp1 191100h1 \([0, 1, 0, -2970053, 2002578423]\) \(-769623354048512/15247889631\) \(-57404766950320608000\) \([]\) \(5544000\) \(2.5843\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 191100.cp1 has rank \(1\).

Complex multiplication

The elliptic curves in class 191100.cp do not have complex multiplication.

Modular form 191100.2.a.cp

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