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Properties

Label 477950.i
Number of curves $1$
Conductor $477950$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("i1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 477950.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 477950.i do not have complex multiplication.

Modular form 477950.2.a.i

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + 2 q^{7} - q^{8} + q^{9} - 2 q^{12} + 5 q^{13} - 2 q^{14} + q^{16} - 5 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 477950.i

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
477950.i1 477950i1 \([1, 0, 1, -1576, -8342952]\) \(-25/1738\) \(-30068095878906250\) \([]\) \(4924800\) \(1.8407\) \(\Gamma_0(N)\)-optimal