Properties

Label 51301b
Number of curves $1$
Conductor $51301$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 51301b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51301.b1 51301b1 \([1, 1, 0, -1699, 27774]\) \(-912673/61\) \(-36284222581\) \([]\) \(48384\) \(0.77819\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51301b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51301b do not have complex multiplication.

Modular form 51301.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 2 q^{6} + q^{7} - 3 q^{8} + q^{9} - 3 q^{10} + 5 q^{11} - 2 q^{12} + q^{13} + q^{14} - 6 q^{15} - q^{16} - 4 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display