Properties

Label 5850.bp
Number of curves $1$
Conductor $5850$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 5850.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.bp1 5850bl1 \([1, -1, 1, -80915, 9430067]\) \(-3214683778008145/238496514048\) \(-4346598968524800\) \([]\) \(30912\) \(1.7495\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5850.bp1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5850.bp do not have complex multiplication.

Modular form 5850.2.a.bp

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 4 q^{11} - q^{13} + q^{16} + q^{19} + O(q^{20})\) Copy content Toggle raw display