Properties

Label 42350bf
Number of curves $1$
Conductor $42350$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 42350bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.u1 42350bf1 \([1, -1, 0, -2492, -161584]\) \(-7243533/43904\) \(-10375750000000\) \([]\) \(60480\) \(1.1812\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42350bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 42350bf do not have complex multiplication.

Modular form 42350.2.a.bf

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