Properties

Label 10051e
Number of curves $1$
Conductor $10051$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10051e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10051.e1 10051e1 \([0, -1, 1, -176, 58753]\) \(-4096/10051\) \(-1487908720339\) \([]\) \(21120\) \(1.0147\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10051e1 has rank \(1\).

Complex multiplication

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

Modular form 10051.2.a.e

sage: E.q_eigenform(10)
 
\(q + 2q^{2} + 2q^{3} + 2q^{4} - q^{5} + 4q^{6} + 3q^{7} + q^{9} - 2q^{10} - 5q^{11} + 4q^{12} - 2q^{13} + 6q^{14} - 2q^{15} - 4q^{16} - 3q^{17} + 2q^{18} + q^{19} + O(q^{20})\)  Toggle raw display