Properties

Label 10051.a
Number of curves $1$
Conductor $10051$
CM no
Rank $1$

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

Elliptic curves in class 10051.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10051.a1 10051d1 \([1, 1, 1, -11, -18]\) \(279841/19\) \(10051\) \([]\) \(336\) \(-0.48344\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10051.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10051.a do not have complex multiplication.

Modular form 10051.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3q^{8} - 2q^{9} + q^{10} - 2q^{11} + q^{12} + 4q^{13} + q^{15} - q^{16} + 3q^{17} + 2q^{18} + q^{19} + O(q^{20})\)  Toggle raw display