Properties

Label 13225.b
Number of curves $1$
Conductor $13225$
CM no
Rank $1$

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

Elliptic curves in class 13225.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13225.b1 13225m1 \([0, 1, 1, -9698, -372186]\) \(-5451776/23\) \(-425603180875\) \([]\) \(29568\) \(1.0860\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13225.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 13225.b do not have complex multiplication.

Modular form 13225.2.a.b

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