Properties

Label 323400.by
Number of curves $1$
Conductor $323400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 323400.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
323400.by1 323400by1 \([0, -1, 0, -16771485208, 403206630846412]\) \(2308702086811951250/1025271882697689\) \(231691144286182793599648800000000\) \([]\) \(1097349120\) \(4.9059\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 323400.by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 323400.by do not have complex multiplication.

Modular form 323400.2.a.by

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - q^{11} + 4 q^{13} + q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display