Properties

Label 5070.r
Number of curves $1$
Conductor $5070$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 5070.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.r1 5070s1 \([1, 1, 1, -16260, 799365]\) \(-2813198004118489/33177600000\) \(-5607014400000\) \([]\) \(16320\) \(1.2588\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5070.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5070.r do not have complex multiplication.

Modular form 5070.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 3 q^{7} + q^{8} + q^{9} + q^{10} + 3 q^{11} - q^{12} - 3 q^{14} - q^{15} + q^{16} + q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display