Properties

Label 85008.m
Number of curves $1$
Conductor $85008$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 85008.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85008.m1 85008br1 \([0, -1, 0, -1856, -304128]\) \(-172715635009/9694992384\) \(-39710688804864\) \([]\) \(168960\) \(1.2893\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 85008.m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 85008.m do not have complex multiplication.

Modular form 85008.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} - q^{11} + 3 q^{13} + q^{15} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display