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Properties

Label 412984.s
Number of curves $1$
Conductor $412984$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("s1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 412984.s1 has rank \(0\).

Complex multiplication

The elliptic curves in class 412984.s do not have complex multiplication.

Modular form 412984.2.a.s

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{3} + 2 q^{5} + 4 q^{7} + q^{9} + q^{11} + q^{13} + 4 q^{15} - 5 q^{17} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 412984.s

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412984.s1 412984s1 \([0, -1, 0, -603712, -180399027]\) \(-32327511017728/10789207\) \(-8121403977701872\) \([]\) \(4769280\) \(2.0255\) \(\Gamma_0(N)\)-optimal