Properties

Label 491970bh
Number of curves $1$
Conductor $491970$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 491970bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
491970.bh1 491970bh1 \([1, 0, 1, -5501995968, -162780420318194]\) \(-124427822010671478697670089/5317924709672681472000\) \(-787243712031462300721348608000\) \([]\) \(1104071760\) \(4.5026\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 491970bh1 has rank \(0\).

Complex multiplication

The elliptic curves in class 491970bh do not have complex multiplication.

Modular form 491970.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 5 q^{11} + q^{12} + 2 q^{13} + q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display