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Properties

Label 422142.ba
Number of curves $1$
Conductor $422142$
CM no
Rank $2$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ba1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 422142.ba1 has rank \(2\).

Complex multiplication

The elliptic curves in class 422142.ba do not have complex multiplication.

Modular form 422142.2.a.ba

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

Elliptic curves in class 422142.ba

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422142.ba1 422142ba1 \([1, 0, 1, -168337, 12258404]\) \(997247786436744313/454115447307648\) \(240227071625745792\) \([]\) \(5569536\) \(2.0300\) \(\Gamma_0(N)\)-optimal