Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 51376z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51376.a1 51376z1 \([0, 0, 0, -165451, 25911418]\) \(-25334470953/9386\) \(-185566942306304\) \([]\) \(612864\) \(1.7054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51376z1 has rank \(1\).

Complex multiplication

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

Modular form 51376.2.a.z

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