Properties

Label 80688.b
Number of curves $1$
Conductor $80688$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 80688.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80688.b1 80688t1 \([0, -1, 0, -30164424, -62696930832]\) \(92806423177/1769472\) \(57872800215135003082752\) \([]\) \(7934976\) \(3.1610\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 80688.b1 has rank \(1\).

Complex multiplication

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

Modular form 80688.2.a.b

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