Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 414736.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
414736.w1 414736w1 \([0, -1, 0, 198728, 206124752]\) \(46\) \(-18868652251800307712\) \([]\) \(7948800\) \(2.3790\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 414736.w1 has rank \(1\).

Complex multiplication

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

Modular form 414736.2.a.w

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