Properties

Label 212160.r
Number of curves $1$
Conductor $212160$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 212160.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212160.r1 212160hj1 \([0, -1, 0, 1149439, 1209726465]\) \(640680045567719039/2783963520000000\) \(-729799332986880000000\) \([]\) \(10063872\) \(2.6858\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 212160.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 212160.r do not have complex multiplication.

Modular form 212160.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} + 3 q^{11} - q^{13} + q^{15} - q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display