Properties

Label 473382cq
Number of curves $1$
Conductor $473382$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 473382cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
473382.cq1 473382cq1 \([1, -1, 0, -261358938, 1635681681972]\) \(-112205650221491190337/745029571313664\) \(-13109754757090885387812864\) \([]\) \(167552000\) \(3.6552\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 473382cq1 has rank \(1\).

Complex multiplication

The elliptic curves in class 473382cq do not have complex multiplication.

Modular form 473382.2.a.cq

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} + q^{7} - q^{8} - 3 q^{10} + q^{11} - q^{13} - q^{14} + q^{16} + q^{19} + O(q^{20})\) Copy content Toggle raw display