Properties

Label 5850.a
Number of curves $1$
Conductor $5850$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 5850.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.a1 5850s1 \([1, -1, 0, 18, -54]\) \(34295/78\) \(-1421550\) \([]\) \(1344\) \(-0.13531\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5850.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5850.a do not have complex multiplication.

Modular form 5850.2.a.a

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