Properties

Label 51376f
Number of curves $1$
Conductor $51376$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 51376f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51376.d1 51376f1 \([0, 1, 0, -1408, 20931]\) \(-4000000/247\) \(-19075549168\) \([]\) \(26880\) \(0.72702\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51376f1 has rank \(2\).

Complex multiplication

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

Modular form 51376.2.a.f

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