Properties

Label 14651n
Number of curves $1$
Conductor $14651$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 14651n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14651.a1 14651n1 \([0, 0, 1, -75019, 11082930]\) \(-396870925750272/221358574619\) \(-26042614945350731\) \([]\) \(357120\) \(1.8532\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 14651n1 has rank \(2\).

Complex multiplication

The elliptic curves in class 14651n do not have complex multiplication.

Modular form 14651.2.a.n

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