Properties

Label 51520.bz
Number of curves $1$
Conductor $51520$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 51520.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51520.bz1 51520s1 \([0, 1, 0, -13105, -581897]\) \(-243090490825984/34514375\) \(-35342720000\) \([]\) \(57344\) \(1.0401\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51520.bz1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51520.bz do not have complex multiplication.

Modular form 51520.2.a.bz

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