Properties

Label 471510.p
Number of curves $1$
Conductor $471510$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 471510.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
471510.p1 471510p1 \([1, -1, 0, -46269105, -121156445539]\) \(-115304327640815067/31726223360\) \(-3014184163718496337920\) \([]\) \(47416320\) \(3.1038\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 471510.p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 471510.p do not have complex multiplication.

Modular form 471510.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 3 q^{11} + q^{16} - 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display