Properties

Label 414736.q
Number of curves $1$
Conductor $414736$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 414736.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
414736.q1 414736q1 \([0, -1, 0, -112324, -14955457]\) \(-562432/23\) \(-6409188944225648\) \([]\) \(2433024\) \(1.8006\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 414736.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 414736.q do not have complex multiplication.

Modular form 414736.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - 2 q^{9} - 2 q^{11} - 7 q^{13} + 2 q^{15} - 4 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display