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Properties

Label 479408f
Number of curves $1$
Conductor $479408$
CM no
Rank $2$

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 479408f1 has rank \(2\).

Complex multiplication

The elliptic curves in class 479408f do not have complex multiplication.

Modular form 479408.2.a.f

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} - q^{7} + q^{9} - q^{11} - 2 q^{13} - 2 q^{15} + q^{17} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 479408f

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
479408.f1 479408f1 \([0, 1, 0, 26955, 873727]\) \(179830784/130891\) \(-1576417896952576\) \([]\) \(1589760\) \(1.6045\) \(\Gamma_0(N)\)-optimal