Properties

Label 51376y
Number of curves $1$
Conductor $51376$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 51376y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51376.f1 51376y1 \([0, 1, 0, -784, 8724]\) \(-77086633/5776\) \(-3998285824\) \([]\) \(41472\) \(0.59098\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51376y1 has rank \(1\).

Complex multiplication

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

Modular form 51376.2.a.y

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