Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("em1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 405600.em

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.em1 405600em1 \([0, 1, 0, 55792, 120720588]\) \(43709080/14348907\) \(-6304909735800000000\) \([]\) \(8812800\) \(2.2865\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 405600.em1 has rank \(1\).

Complex multiplication

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

Modular form 405600.2.a.em

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{7} + q^{9} + 4 q^{11} + 6 q^{17} + 7 q^{19} + O(q^{20})\)  Toggle raw display