Properties

Label 102541a
Number of curves $1$
Conductor $102541$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 102541a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102541.a1 102541a1 \([1, 1, 1, -3397, 79072]\) \(-912673/61\) \(-289756358701\) \([]\) \(139120\) \(0.95133\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 102541a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 102541a do not have complex multiplication.

Modular form 102541.2.a.a

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