Properties

Label 406203.b
Number of curves $1$
Conductor $406203$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 406203.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
406203.b1 406203b1 \([0, -1, 1, -81016, -10330416]\) \(-98867482624/20696067\) \(-12310503304578507\) \([]\) \(7526400\) \(1.8092\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 406203.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 406203.b do not have complex multiplication.

Modular form 406203.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} - q^{7} + q^{9} - 8 q^{10} + 5 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} - 4 q^{15} - 4 q^{16} - 2 q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display