Properties

Label 80688bf
Number of curves $1$
Conductor $80688$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 80688bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80688.v1 80688bf1 \([0, 1, 0, 17931, -47646513]\) \(524288/807003\) \(-981337183436729088\) \([]\) \(1451520\) \(2.1313\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 80688bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 80688bf do not have complex multiplication.

Modular form 80688.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - 4 q^{7} + q^{9} - 5 q^{11} - 4 q^{13} - 2 q^{15} + 5 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display