Properties

Label 34969.b
Number of curves $1$
Conductor $34969$
CM no
Rank $2$

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

Elliptic curves in class 34969.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34969.b1 34969j1 \([0, 0, 1, 244783, -8174004]\) \(37933056/22627\) \(-967557126528354043\) \([]\) \(1036800\) \(2.1404\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 34969.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 34969.b do not have complex multiplication.

Modular form 34969.2.a.b

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