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Properties

Label 486720kc
Number of curves $1$
Conductor $486720$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("kc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 486720kc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 486720kc do not have complex multiplication.

Modular form 486720.2.a.kc

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

Elliptic curves in class 486720kc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
486720.kc1 486720kc1 \([0, 0, 0, -342732, -77000456]\) \(7311616/25\) \(15223493007590400\) \([]\) \(4792320\) \(1.9686\) \(\Gamma_0(N)\)-optimal