Properties

Label 57498.g
Number of curves $1$
Conductor $57498$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 57498.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57498.g1 57498f1 \([1, 1, 0, -9611, 406437]\) \(-38272753/6216\) \(-15948555358344\) \([]\) \(196992\) \(1.2610\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57498.g1 has rank \(0\).

Complex multiplication

The elliptic curves in class 57498.g do not have complex multiplication.

Modular form 57498.2.a.g

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