Properties

Label 452425.b
Number of curves $1$
Conductor $452425$
CM no
Rank $2$

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

Elliptic curves in class 452425.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
452425.b1 452425b1 \([1, 0, 1, -251, 1273]\) \(111284641/18097\) \(282765625\) \([]\) \(172800\) \(0.34360\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 452425.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 452425.b do not have complex multiplication.

Modular form 452425.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} + q^{7} - 3 q^{8} - 2 q^{9} - 6 q^{11} - q^{12} + 5 q^{13} + q^{14} - q^{16} + 7 q^{17} - 2 q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display