Properties

Label 112530.by
Number of curves $1$
Conductor $112530$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 112530.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112530.by1 112530cd1 \([1, 1, 1, 11795, -265693]\) \(102437538839/77137920\) \(-136654530693120\) \([]\) \(594000\) \(1.4005\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 112530.by1 has rank \(0\).

Complex multiplication

The elliptic curves in class 112530.by do not have complex multiplication.

Modular form 112530.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 3 q^{7} + q^{8} + q^{9} + q^{10} - q^{12} + 2 q^{13} - 3 q^{14} - q^{15} + q^{16} - 8 q^{17} + q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display