Properties

Label 252700.w
Number of curves $1$
Conductor $252700$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 252700.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
252700.w1 252700w1 \([0, 0, 0, -45125, -4286875]\) \(-34560/7\) \(-2058257293750000\) \([]\) \(1179360\) \(1.6609\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 252700.w1 has rank \(2\).

Complex multiplication

The elliptic curves in class 252700.w do not have complex multiplication.

Modular form 252700.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3 q^{9} - 5 q^{11} - 6 q^{13} - 4 q^{17} + O(q^{20})\) Copy content Toggle raw display