Properties

Label 212160fk
Number of curves $1$
Conductor $212160$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fk1")
 
E.isogeny_class()
 

Elliptic curves in class 212160fk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212160.ei1 212160fk1 \([0, 1, 0, -565761, -312908961]\) \(-152796558778456322/233895263671875\) \(-30657120000000000000\) \([]\) \(4792320\) \(2.4306\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 212160fk1 has rank \(1\).

Complex multiplication

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

Modular form 212160.2.a.fk

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