Properties

Label 412224j
Number of curves $1$
Conductor $412224$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 412224j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412224.j1 412224j1 \([0, -1, 0, -3681, -160461]\) \(-86210302283776/126575253531\) \(-8100816225984\) \([]\) \(604800\) \(1.1688\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 412224j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 412224j do not have complex multiplication.

Modular form 412224.2.a.j

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