Properties

Label 57222.h
Number of curves $1$
Conductor $57222$
CM no
Rank $0$

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

Elliptic curves in class 57222.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57222.h1 57222bc1 \([1, -1, 0, -12183965793, -517805967176451]\) \(-39334245666480232823953/14521637786211072\) \(-73847279252305447818727742208\) \([]\) \(131604480\) \(4.5070\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57222.h1 has rank \(0\).

Complex multiplication

The elliptic curves in class 57222.h do not have complex multiplication.

Modular form 57222.2.a.h

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