Properties

Label 817.a
Number of curves $1$
Conductor $817$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 817.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
817.a1 817a1 \([0, 1, 1, 1, 6]\) \(32768/15523\) \(-15523\) \([]\) \(56\) \(-0.51674\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 817.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 817.a do not have complex multiplication.

Modular form 817.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{7} + q^{9} - 5 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{15} + 4 q^{16} - 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display