Properties

Label 489762bc
Number of curves $1$
Conductor $489762$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 489762bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
489762.bc1 489762bc1 \([1, -1, 0, -354600, 59835712]\) \(40024541162402329/10645281916416\) \(1311509377384367616\) \([]\) \(7520256\) \(2.1849\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 489762bc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 489762bc do not have complex multiplication.

Modular form 489762.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 3 q^{11} + q^{14} + q^{16} - 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display