Properties

Label 466578.f
Number of curves $1$
Conductor $466578$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 466578.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466578.f1 466578f1 \([1, -1, 0, -1091786271, -13885004340019]\) \(-1008050316336685251/23552\) \(-3362653987217150976\) \([]\) \(106444800\) \(3.5284\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 466578.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 466578.f do not have complex multiplication.

Modular form 466578.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{8} + 3 q^{10} - 4 q^{11} + 3 q^{13} + q^{16} + 3 q^{17} + O(q^{20})\) Copy content Toggle raw display