Properties

Label 414736r
Number of curves $1$
Conductor $414736$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 414736r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
414736.r1 414736r1 \([0, -1, 0, 376, -17072]\) \(46\) \(-127459985408\) \([]\) \(345600\) \(0.81121\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 414736r1 has rank \(1\).

Complex multiplication

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

Modular form 414736.2.a.r

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