Properties

Label 8712.p
Number of curves $1$
Conductor $8712$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 8712.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8712.p1 8712x1 \([0, 0, 0, 243573, -17012842]\) \(9987164/6561\) \(-1049878407882433536\) \([]\) \(67584\) \(2.1468\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8712.p1 has rank \(0\).

Complex multiplication

The elliptic curves in class 8712.p do not have complex multiplication.

Modular form 8712.2.a.p

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