Properties

Label 123840.em
Number of curves $1$
Conductor $123840$
CM no
Rank $1$

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

Elliptic curves in class 123840.em

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123840.em1 123840cq1 \([0, 0, 0, -167232, -26414944]\) \(-43304636317696/176326875\) \(-2106036910080000\) \([]\) \(786432\) \(1.7965\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 123840.em1 has rank \(1\).

Complex multiplication

The elliptic curves in class 123840.em do not have complex multiplication.

Modular form 123840.2.a.em

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2 q^{7} + q^{11} + 5 q^{13} + 3 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display