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Properties

Label 457776.et
Number of curves $1$
Conductor $457776$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("et1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 457776.et1 has rank \(1\).

Complex multiplication

The elliptic curves in class 457776.et do not have complex multiplication.

Modular form 457776.2.a.et

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{5} - q^{7} + q^{11} + 3 q^{13} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 457776.et

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457776.et1 457776et1 \([0, 0, 0, -84099, 263846018]\) \(-263762497/120434688\) \(-30035492230064504832\) \([]\) \(6635520\) \(2.4165\) \(\Gamma_0(N)\)-optimal