Properties

Label 414400.bd
Number of curves $1$
Conductor $414400$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 414400.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
414400.bd1 414400bd1 \([0, 1, 0, 27967, 676063]\) \(4724717752/3109295\) \(-1591959040000000\) \([]\) \(1382400\) \(1.6058\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 414400.bd1 has rank \(2\).

Complex multiplication

The elliptic curves in class 414400.bd do not have complex multiplication.

Modular form 414400.2.a.bd

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{7} + q^{9} - 2 q^{11} + q^{13} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display