Properties

Label 259182.ew
Number of curves $1$
Conductor $259182$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ew1")
 
E.isogeny_class()
 

Elliptic curves in class 259182.ew

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.ew1 259182ew1 \([1, -1, 1, -36752, -2702653]\) \(-5657831164259/1904\) \(-1847449296\) \([]\) \(562176\) \(1.1356\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259182.ew1 has rank \(1\).

Complex multiplication

The elliptic curves in class 259182.ew do not have complex multiplication.

Modular form 259182.2.a.ew

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - q^{13} - q^{14} + q^{16} - q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display