Properties

Label 5056.h
Number of curves $1$
Conductor $5056$
CM no
Rank $1$

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

Elliptic curves in class 5056.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5056.h1 5056q1 \([0, -1, 0, -225, -1151]\) \(4826809/316\) \(82837504\) \([]\) \(1536\) \(0.26916\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5056.h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5056.h do not have complex multiplication.

Modular form 5056.2.a.h

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