Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 57498.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57498.h1 57498l1 \([1, 0, 1, 45, 2350]\) \(7599023/1741824\) \(-2384557056\) \([]\) \(50400\) \(0.47856\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57498.h1 has rank \(1\).

Complex multiplication

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

Modular form 57498.2.a.h

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