Properties

Label 130130.b
Number of curves $1$
Conductor $130130$
CM no
Rank $0$

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

Elliptic curves in class 130130.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130130.b1 130130b1 \([1, -1, 0, -77405665, 319294236925]\) \(-372056100892249761/104122726400000\) \(-14354202028710057113600000\) \([]\) \(83865600\) \(3.5427\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 130130.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 130130.b do not have complex multiplication.

Modular form 130130.2.a.b

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