Properties

Label 997c
Number of curves $1$
Conductor $997$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 997c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
997.a1 997c1 \([0, -1, 1, -24, 54]\) \(1593413632/997\) \(997\) \([]\) \(96\) \(-0.48278\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 997c1 has rank \(2\).

Complex multiplication

The elliptic curves in class 997c do not have complex multiplication.

Modular form 997.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{9} + 4 q^{10} - 2 q^{11} - 2 q^{12} - q^{13} + 8 q^{14} + 2 q^{15} - 4 q^{16} - 6 q^{17} + 4 q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display