Properties

Label 418761e
Number of curves $1$
Conductor $418761$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 418761e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
418761.e1 418761e1 \([0, 0, 1, -250563, 56333686]\) \(-98867482624/20696067\) \(-364173951280778667\) \([]\) \(12441600\) \(2.0914\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 418761e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 418761e do not have complex multiplication.

Modular form 418761.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} + 4 q^{5} + q^{7} - 8 q^{10} - 5 q^{11} - 2 q^{13} - 2 q^{14} - 4 q^{16} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display