Properties

Label 504521.b
Number of curves $1$
Conductor $504521$
CM no
Rank $2$

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

Elliptic curves in class 504521.b

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
504521.b1 \([1, 0, 1, -5, -35]\) \(-10218313/504521\) \(-504521\) \([]\) \(99904\) \(-0.22575\)

Rank

sage: E.rank()
 

The elliptic curve 504521.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 504521.b do not have complex multiplication.

Modular form 504521.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} - 3 q^{5} + q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} - 5 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} + 8 q^{17} - 2 q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display