Properties

Label 300042.b
Number of curves $1$
Conductor $300042$
CM no
Rank $2$

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

Elliptic curves in class 300042.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
300042.b1 300042b1 \([1, -1, 0, -105, 439]\) \(4767078987/33338\) \(900126\) \([]\) \(43520\) \(-0.024434\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 300042.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 300042.b do not have complex multiplication.

Modular form 300042.2.a.b

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