Properties

Label 474320.cr
Number of curves $1$
Conductor $474320$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 474320.cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
474320.cr1 474320cr1 \([0, -1, 0, 1272759, -1733694059]\) \(12459008/78125\) \(-1429777527410540000000\) \([]\) \(16934400\) \(2.7411\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 474320.cr1 has rank \(1\).

Complex multiplication

The elliptic curves in class 474320.cr do not have complex multiplication.

Modular form 474320.2.a.cr

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{9} + q^{13} + q^{15} - 5 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display