Properties

Label 84966.ed
Number of curves $1$
Conductor $84966$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 84966.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.ed1 84966ed1 \([1, 0, 0, 13866, -752508]\) \(30004847/42336\) \(-416000399893344\) \([]\) \(414720\) \(1.4907\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 84966.ed1 has rank \(1\).

Complex multiplication

The elliptic curves in class 84966.ed do not have complex multiplication.

Modular form 84966.2.a.ed

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} + q^{8} + q^{9} + 3 q^{10} + q^{11} + q^{12} - 4 q^{13} + 3 q^{15} + q^{16} + q^{18} + O(q^{20})\) Copy content Toggle raw display