Properties

Label 481338.r
Number of curves $1$
Conductor $481338$
CM no
Rank $1$

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

Elliptic curves in class 481338.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
481338.r1 481338r1 \([1, -1, 0, 13590, -4886568]\) \(26005537679/980187156\) \(-10461820790076084\) \([]\) \(2801664\) \(1.7538\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 481338.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 481338.r do not have complex multiplication.

Modular form 481338.2.a.r

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