Properties

Label 51376.g
Number of curves $1$
Conductor $51376$
CM no
Rank $0$

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

Elliptic curves in class 51376.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51376.g1 51376bc1 \([0, -1, 0, -273472, 511376384]\) \(-251347109804029/12403865550848\) \(-111621294551912677376\) \([]\) \(1048320\) \(2.5268\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51376.g1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51376.g do not have complex multiplication.

Modular form 51376.2.a.g

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