Properties

Label 234416.k
Number of curves $1$
Conductor $234416$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 234416.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234416.k1 234416k1 \([0, -1, 0, -10992, -456896]\) \(-304821217/13754\) \(-6627919241216\) \([]\) \(380160\) \(1.2245\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 234416.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 234416.k do not have complex multiplication.

Modular form 234416.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} - 2 q^{9} - 2 q^{11} + q^{13} + 3 q^{15} + q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display