Properties

Label 87856r
Number of curves $1$
Conductor $87856$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 87856r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87856.r1 87856r1 \([0, -1, 0, -6165, 189113]\) \(-4194304/19\) \(-117405135616\) \([]\) \(120960\) \(0.97568\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 87856r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 87856r do not have complex multiplication.

Modular form 87856.2.a.r

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} - 3 q^{7} + q^{9} + 5 q^{11} - 4 q^{13} + 2 q^{15} + q^{19} + O(q^{20})\) Copy content Toggle raw display