Properties

Label 455175bc
Number of curves $1$
Conductor $455175$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 455175bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
455175.bc1 455175bc1 \([1, -1, 1, -2823440, -3087704968]\) \(-1151731985/1240029\) \(-2680030097613128576925\) \([]\) \(17233920\) \(2.8066\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 455175bc1 has rank \(2\).

Complex multiplication

The elliptic curves in class 455175bc do not have complex multiplication.

Modular form 455175.2.a.bc

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