Properties

Label 111573.x
Number of curves $1$
Conductor $111573$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 111573.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111573.x1 111573r1 \([1, -1, 0, -632256, 83357441]\) \(950152003191/448204933\) \(13185193891150888299\) \([]\) \(2283008\) \(2.3630\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 111573.x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 111573.x do not have complex multiplication.

Modular form 111573.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{5} - 3 q^{8} - 3 q^{10} - q^{11} + q^{13} - q^{16} - 6 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display