Properties

Label 8050k
Number of curves $1$
Conductor $8050$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 8050k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8050.f1 8050k1 \([1, -1, 0, 23008, 316416]\) \(137927116575/84410368\) \(-824320000000000\) \([]\) \(36480\) \(1.5513\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8050k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8050k do not have complex multiplication.

Modular form 8050.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} - 4 q^{11} - q^{13} - q^{14} + q^{16} - 3 q^{17} + 3 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display