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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("a1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 477950.a1 has rank \(1\).

Complex multiplication

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

Modular form 477950.2.a.a

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

Elliptic curves in class 477950.a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
477950.a1 477950a1 \([1, -1, 0, -67603267, 213232957141]\) \(1234384987853171097/4851295584256\) \(134286969633439744000000\) \([]\) \(91238400\) \(3.2953\) \(\Gamma_0(N)\)-optimal