Properties

Label 457776x
Number of curves $1$
Conductor $457776$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 457776x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457776.x1 457776x1 \([0, 0, 0, 204, 18479]\) \(278528/43923\) \(-148059865008\) \([]\) \(359424\) \(0.82270\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 457776x1 has rank \(2\).

Complex multiplication

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

Modular form 457776.2.a.x

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