Properties

Label 282064.e
Number of curves $1$
Conductor $282064$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 282064.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
282064.e1 282064e1 \([0, 1, 0, -9344, -370316]\) \(-912673/61\) \(-6030916440064\) \([]\) \(630784\) \(1.2043\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 282064.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 282064.e do not have complex multiplication.

Modular form 282064.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 3 q^{5} + q^{7} + q^{9} - 5 q^{11} + q^{13} - 6 q^{15} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display