Properties

Label 57498o
Number of curves $1$
Conductor $57498$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 57498o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57498.n1 57498o1 \([1, 1, 1, 71844, -36892995]\) \(15983964359/238793856\) \(-612679702646143104\) \([]\) \(766080\) \(2.0937\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57498o1 has rank \(1\).

Complex multiplication

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

Modular form 57498.2.a.o

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