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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("r1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 479408.r1 has rank \(2\).

Complex multiplication

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

Modular form 479408.2.a.r

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

Elliptic curves in class 479408.r

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
479408.r1 479408r1 \([0, 1, 0, -1032, 12419]\) \(21064753408/6889\) \(39790864\) \([]\) \(191232\) \(0.43195\) \(\Gamma_0(N)\)-optimal