Properties

Label 200400cr
Number of curves $1$
Conductor $200400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 200400cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200400.h1 200400cr1 \([0, -1, 0, -188, 1047]\) \(369381632/4509\) \(9018000\) \([]\) \(35328\) \(0.14508\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 200400cr1 has rank \(1\).

Complex multiplication

The elliptic curves in class 200400cr do not have complex multiplication.

Modular form 200400.2.a.cr

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} - 2 q^{11} + q^{13} - 2 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display