Properties

Label 4200s
Number of curves $1$
Conductor $4200$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 4200s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4200.m1 4200s1 \([0, -1, 0, -8, 57]\) \(-160000/3087\) \(-1234800\) \([]\) \(576\) \(-0.15014\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4200s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4200s do not have complex multiplication.

Modular form 4200.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 3 q^{11} + 2 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display