Properties

Label 405600.e
Number of curves $1$
Conductor $405600$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 405600.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.e1 405600e1 \([0, -1, 0, 81792, 23267412]\) \(358066904/1594323\) \(-269440587000000000\) \([]\) \(4692480\) \(2.0271\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 405600.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 405600.e do not have complex multiplication.

Modular form 405600.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} - q^{11} + 6q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display