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Properties

Label 412984l
Number of curves $1$
Conductor $412984$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("l1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 412984l1 has rank \(1\).

Complex multiplication

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

Modular form 412984.2.a.l

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

Elliptic curves in class 412984l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412984.l1 412984l1 \([0, 1, 0, -16004, 829685]\) \(-1668352/143\) \(-38858392237808\) \([]\) \(1428192\) \(1.3522\) \(\Gamma_0(N)\)-optimal